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Theorem equcomd 1683
Description: Deduction form of equcom 1682, symmetry of equality. For the versions for classes, see eqcom 2141 and eqcomd 2145. (Contributed by BJ, 6-Oct-2019.)
Hypothesis
Ref Expression
equcomd.1  |-  ( ph  ->  x  =  y )
Assertion
Ref Expression
equcomd  |-  ( ph  ->  y  =  x )

Proof of Theorem equcomd
StepHypRef Expression
1 equcomd.1 . 2  |-  ( ph  ->  x  =  y )
2 equcom 1682 . 2  |-  ( x  =  y  <->  y  =  x )
31, 2sylib 121 1  |-  ( ph  ->  y  =  x )
Colors of variables: wff set class
Syntax hints:    -> wi 4
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 1425  ax-ie2 1470  ax-8 1482  ax-17 1506  ax-i9 1510
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  fisumcom2  11219  trirec0  13323
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