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Theorem hbnaes 2065
Description: Rule that applies hbnae 2063 to antecedent. (Contributed by NM, 15-May-1993.)
Hypothesis
Ref Expression
hbnaes.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 2063 . 2  |-  ( -. 
A. x  x  =  y  ->  A. z  -.  A. x  x  =  y )
2 hbnaes.1 . 2  |-  ( A. z  -.  A. x  x  =  y  ->  ph )
31, 2syl 16 1  |-  ( -. 
A. x  x  =  y  ->  ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1397
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-5 1712  ax-6 1755  ax-7 1798  ax-10 1845  ax-11 1850  ax-12 1862  ax-13 2006
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1621  df-nf 1625
This theorem is referenced by: (None)
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