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Theorem equcomi 1648
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 1646 . 2  |-  x  =  x
2 ax-8 1645 . 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  1649  equequ1  1650  equcoms  1653  ax12dgen2  1702  sp  1718  dvelimhw  1737  ax12olem1  1870  ax10  1886  a16g  1887  cbv2h  1922  equvini  1929  equveli  1930  equsb2  1977  ax16i  1988  aecom-o  2092  ax10from10o  2118  aev-o  2123  axsep  4142  rext  4224  iotaval  5232  soxp  6230  axextnd  8215  inpc  25288  finminlem  26242  hbae-x12  29182  a12stdy2-x12  29185  equvinv  29187  equvelv  29189  ax10lem18ALT  29197  a12study  29205  a12study3  29208  a12study10n  29210
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645
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