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Theorem nalequcoms 1407
Description: A commutation rule for distinct variable specifiers. (Contributed by NM, 2-Jan-2002.) (Revised by Mario Carneiro, 2-Feb-2015.)
Hypothesis
Ref Expression
nalequcoms.1 x x = yφ)
Assertion
Ref Expression
nalequcoms y y = xφ)

Proof of Theorem nalequcoms
StepHypRef Expression
1 alequcom 1405 . . 3 (x x = yy y = x)
21con3i 561 . 2 y y = x → ¬ x x = y)
3 nalequcoms.1 . 2 x x = yφ)
42, 3syl 14 1 y y = xφ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wal 1240   = wceq 1242
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 544  ax-in2 545  ax-10 1393
This theorem is referenced by:  nd5  1696
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