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Theorem equequ1 1640
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 1436 . 2  |-  ( x  =  y  ->  (
x  =  z  -> 
y  =  z ) )
2 equtr 1637 . 2  |-  ( x  =  y  ->  (
y  =  z  ->  x  =  z )
)
31, 2impbid 127 1  |-  ( x  =  y  ->  (
x  =  z  <->  y  =  z ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1379  ax-ie2 1424  ax-8 1436  ax-17 1460  ax-i9 1464
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  equveli  1684  drsb1  1722  equsb3lem  1867  euequ1  2038  axext3  2066  reu6  2790  reu7  2796  cbviota  4922  dff13f  5461  poxp  5904  dcdifsnid  6166  supmoti  6500  isoti  6514
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