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Theorem alequcom 1888
Description: Commutation law for identical variable specifiers. The antecedent and consequent are true when  x and  y are substituted with the same variable. Lemma L12 in [Megill] p. 445 (p. 12 of the preprint). (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
alequcom  |-  ( A. x  x  =  y  ->  A. y  y  =  x )

Proof of Theorem alequcom
StepHypRef Expression
1 ax10 1886 1  |-  ( A. x  x  =  y  ->  A. y  y  =  x )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527
This theorem is referenced by:  alequcoms  1889  nalequcoms  1890  aev  1934  sbcom  2028  a12stdy2  28406
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 1636  ax-8 1644  ax-6 1704  ax-7 1709  ax-11 1716  ax-12 1868
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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