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Theorem equequ2 1599
Description: An equivalence law for equality. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
equequ2  |-  ( x  =  y  ->  (
z  =  x  <->  z  =  y ) )

Proof of Theorem equequ2
StepHypRef Expression
1 equtrr 1596 . 2  |-  ( x  =  y  ->  (
z  =  x  -> 
z  =  y ) )
2 equtrr 1596 . . 3  |-  ( y  =  x  ->  (
z  =  y  -> 
z  =  x ) )
32equcoms 1594 . 2  |-  ( x  =  y  ->  (
z  =  y  -> 
z  =  x ) )
41, 3impbid 120 1  |-  ( x  =  y  ->  (
z  =  x  <->  z  =  y ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1338  ax-ie2 1383  ax-8 1395  ax-17 1419  ax-i9 1423
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  ax11v2  1701  ax11v  1708  ax11ev  1709  equs5or  1711  eujust  1902  euf  1905  mo23  1941  iotaval  4878  dffun4f  4918  dff13f  5409
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