Metamath Proof Explorer 
< Previous
Next >
Nearby theorems 

Mirrors > Home > MPE Home > Th. List > stdpc6  Unicode version 
Description: One of the two equality axioms of standard predicate calculus, called reflexivity of equality. (The other one is stdpc7 1858.) 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 
Step  Hyp  Ref  Expression 

1  equid 1644  . 2  
2  1  axgen 1533  1 
Colors of variables: wff set class 
Syntax hints: wal 1527 
This theorem is referenced by: cbv3h 1923 
This theorem was proved from axioms: ax1 5 ax2 6 ax3 7 axmp 8 axgen 1533 ax5 1544 ax17 1603 ax9 1635 ax8 1643 
Copyright terms: Public domain  W3C validator 