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Theorem equcomi 1646
Description: Commutative law for equality. Lemma 3 of [KalishMontague] p. 85. See also Lemma 7 of [Tarski] p. 69. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 9-Apr-2017.)
Assertion
Ref Expression
equcomi  |-  ( x  =  y  ->  y  =  x )

Proof of Theorem equcomi
StepHypRef Expression
1 equid 1644 . 2  |-  x  =  x
2 ax-8 1643 . 2  |-  ( x  =  y  ->  (
x  =  x  -> 
y  =  x ) )
31, 2mpi 16 1  |-  ( x  =  y  ->  y  =  x )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  equcom  1647  equequ1  1648  equcoms  1651  ax12dgen2  1700  sp  1716  dvelimhw  1735  ax12olem1  1868  ax10  1884  a16g  1885  cbv2h  1920  equvini  1927  equveli  1928  equsb2  1975  ax16i  1986  aecom-o  2090  ax10from10o  2116  aev-o  2121  axsep  4140  rext  4222  iotaval  5230  soxp  6228  axextnd  8213  inpc  25277  finminlem  26231  hbae-x12  29109  a12stdy2-x12  29112  equvinv  29114  equvelv  29116  ax10lem18ALT  29124  a12study  29132  a12study3  29135  a12study10n  29137
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643
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