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Theorem equcomi 1822
Description: Commutative law for equality. Lemma 7 of [Tarski] p. 69. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 28-Nov-2013.)
Assertion
Ref Expression
equcomi  |-  ( x  =  y  ->  y  =  x )

Proof of Theorem equcomi
StepHypRef Expression
1 equid1 1820 . 2  |-  x  =  x
2 ax-8 1623 . 2  |-  ( x  =  y  ->  (
x  =  x  -> 
y  =  x ) )
31, 2mpi 18 1  |-  ( x  =  y  ->  y  =  x )
Colors of variables: wff set class
Syntax hints:    -> wi 6
This theorem is referenced by:  equcom  1824  equcoms  1825  ax10from10o  1836  cbv2h  1872  equvini  1879  equveli  1880  equsb2  1907  aev  1923  aev-o  1924  axsep  4037  rext  4116  soxp  6080  iotaval  6154  axextnd  8093  inpc  24443  finminlem  25397  a12study  27821  a12study3  27824
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-8 1623  ax-17 1628  ax-9 1684  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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