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Theorem hbnaes 1957
Description: Rule that applies hbnae 1955 to antecedent. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
hbnalequs.1 (z ¬ x x = yφ)
Assertion
Ref Expression
hbnaes x x = yφ)

Proof of Theorem hbnaes
StepHypRef Expression
1 hbnae 1955 . 2 x x = yz ¬ x x = y)
2 hbnalequs.1 . 2 (z ¬ x x = yφ)
31, 2syl 15 1 x x = yφ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545
This theorem is referenced by:  sbal1  2126
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