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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 250 | . 2 ⊢ (𝑥 ∈ 𝐴 ↔ 𝑥 ∈ 𝐴) | |
2 | 1 | eqriv 2607 | 1 ⊢ 𝐴 = 𝐴 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ∈ wcel 1977 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-cleq 2603 |
This theorem is referenced by: (None) |
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