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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 260 | . 2 ⊢ (𝑥 ∈ 𝐴 ↔ 𝑥 ∈ 𝐴) | |
2 | 1 | eqriv 2735 | 1 ⊢ 𝐴 = 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1539 ∈ wcel 2106 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1913 ax-6 1971 ax-7 2011 ax-9 2116 ax-ext 2709 |
This theorem depends on definitions: df-bi 206 df-an 397 df-ex 1783 df-cleq 2730 |
This theorem is referenced by: (None) |
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