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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 261 | . 2 ⊢ (𝑥 ∈ 𝐴 ↔ 𝑥 ∈ 𝐴) | |
2 | 1 | eqriv 2721 | 1 ⊢ 𝐴 = 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ∈ wcel 2098 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-9 2108 ax-ext 2695 |
This theorem depends on definitions: df-bi 206 df-an 396 df-ex 1774 df-cleq 2716 |
This theorem is referenced by: (None) |
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