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Theorem equequ1 1673
Description: An equivalence law for equality. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
equequ1  |-  ( x  =  y  ->  (
x  =  z  <->  y  =  z ) )

Proof of Theorem equequ1
StepHypRef Expression
1 ax-8 1467 . 2  |-  ( x  =  y  ->  (
x  =  z  -> 
y  =  z ) )
2 equtr 1670 . 2  |-  ( x  =  y  ->  (
y  =  z  ->  x  =  z )
)
31, 2impbid 128 1  |-  ( x  =  y  ->  (
x  =  z  <->  y  =  z ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1410  ax-ie2 1455  ax-8 1467  ax-17 1491  ax-i9 1495
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  equveli  1717  drsb1  1755  equsb3lem  1901  euequ1  2072  axext3  2100  reu6  2846  reu7  2852  disjiun  3894  cbviota  5063  dff13f  5639  poxp  6097  dcdifsnid  6368  supmoti  6848  isoti  6862  fsum2dlemstep  11171  ennnfonelemr  11863  ctinf  11870
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