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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 2734 | 1 ⊢ 𝐴 = 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ∈ wcel 2107 |
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 1914 ax-6 1972 ax-7 2012 ax-9 2117 ax-ext 2708 |
This theorem depends on definitions: df-bi 206 df-an 398 df-ex 1783 df-cleq 2729 |
This theorem is referenced by: (None) |
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