Cognitive Scaffold

Preparing your thinking workspace

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MENTAL MODEL · M7383

Substitution Axiom

Substitution Axiom
StructureHigh supportLogic
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Version 1.0.0 · Updated 2026-07-30

CORE DEFINITION

If a = b, then b can be substituted for a in any expression.

SCAFFOLDING EFFECT

psychology

Reduce cognitive load

Equivalent substitution is a fundamental operation in logical reasoning.

anchor

Anchor fast decisions

Substitution of equals is a basic property of equality: if a = b, then in any proposition/expression containing a, a can be replaced by b without changing the truth value; it is a fundamental rule for reasoning, simplification, and proof (reflecting Leibniz's principle of the identity of indiscernibles and the substitutability of identicals).

MINIMUM ACTION

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Source support: Explicit

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    zh.wikipedia.orghttps://zh.wikipedia.org/wiki/%E6%9B%BF%E4%BB%A3%E5%85%AC%E7%90%86ZH · Explicit
    verified

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An informal fallacy that treats limited similarities as establishing equivalence while ignoring differences relevant to the conclusion.

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How many steps of logical reasoning you must go through to get from what the audience already knows to the conclusion you want to convey.

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