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Theorem hbnaes 2046
Description: Rule that applies hbnae 2044 to antecedent. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
hbnalequs.1  |-  ( A. z  -.  A. x  x  =  y  ->  ph )
Assertion
Ref Expression
hbnaes  |-  ( -. 
A. x  x  =  y  ->  ph )

Proof of Theorem hbnaes
StepHypRef Expression
1 hbnae 2044 . 2  |-  ( -. 
A. x  x  =  y  ->  A. z  -.  A. x  x  =  y )
2 hbnalequs.1 . 2  |-  ( A. z  -.  A. x  x  =  y  ->  ph )
31, 2syl 16 1  |-  ( -. 
A. x  x  =  y  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1550
This theorem is referenced by:  sbal1  2204
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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