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Theorem naecoms-o 2178
 Description: A commutation rule for distinct variable specifiers. Version of naecoms 1948 using ax-10o 2139. (Contributed by NM, 2-Jan-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
nalequcoms-o.1 x x = yφ)
Assertion
Ref Expression
naecoms-o y y = xφ)

Proof of Theorem naecoms-o
StepHypRef Expression
1 aecom-o 2151 . . 3 (x x = yy y = x)
2 nalequcoms-o.1 . . 3 x x = yφ)
31, 2nsyl4 134 . 2 φy y = x)
43con1i 121 1 y y = xφ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-10o 2139 This theorem depends on definitions:  df-bi 177  df-ex 1542 This theorem is referenced by:  ax11inda2ALT  2198
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