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Mirrors > Home > ILE Home > Th. List > stdpc6  Structured version GIF version 
Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1635.) 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, 16Feb2005.) 
Ref  Expression 

stdpc6  ⊢ ∀x x = x 
Step  Hyp  Ref  Expression 

1  equid 1571  . 2 ⊢ x = x  
2  1  axgen 1318  1 ⊢ ∀x x = x 
Colors of variables: wff set class 
Syntax hints: ∀wal 1226 
This theorem was proved from axioms: ax1 5 ax2 6 axmp 7 axia1 99 axgen 1318 axie2 1364 ax8 1376 ax17 1400 axi9 1404 
This theorem depends on definitions: dfbi 110 
This theorem is referenced by: (None) 
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