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| Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 2249.) Axiom 6 of [Mendelson] p. 95. Mendelson doesn't say why he prepended the redundant quantifier, but it was probably to be compatible with free logic (which is valid in the empty domain). (Contributed by NM, 16-Feb-2005.) | 
| Ref | Expression | 
|---|---|
| stdpc6 | ⊢ ∀𝑥 𝑥 = 𝑥 | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | equid 2010 | . 2 ⊢ 𝑥 = 𝑥 | |
| 2 | 1 | ax-gen 1794 | 1 ⊢ ∀𝑥 𝑥 = 𝑥 | 
| Colors of variables: wff setvar class | 
| Syntax hints: ∀wal 1537 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 | 
| This theorem depends on definitions: df-bi 207 df-ex 1779 | 
| This theorem is referenced by: (None) | 
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