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Mirrors > Home > MPE Home > Th. List > eqid1 | Structured version Visualization version GIF version |
Description: Law of identity
(reflexivity of class equality). Theorem 6.4 of [Quine]
p. 41.
This law is thought to have originated with Aristotle (Metaphysics, Book VII, Part 17). It is one of the three axioms of Ayn Rand's philosophy (Atlas Shrugged, Part Three, Chapter VII). While some have proposed extending Rand's axiomatization to include Compassion and Kindness, others fear that such an extension may flirt with logical inconsistency. (Contributed by Stefan Allan, 1-Apr-2009.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
eqid1 | ⊢ 𝐴 = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biid 263 | . 2 ⊢ (𝑥 ∈ 𝐴 ↔ 𝑥 ∈ 𝐴) | |
2 | 1 | eqriv 2818 | 1 ⊢ 𝐴 = 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ∈ wcel 2110 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-9 2120 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1777 df-cleq 2814 |
This theorem is referenced by: (None) |
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