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Theorem hbnaes 1733
Description: Rule that applies hbnae 1731 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 1731 . 2  |-  ( -. 
A. x  x  =  y  ->  A. z  -.  A. x  x  =  y )
2 hbnalequs.1 . 2  |-  ( A. z  -.  A. x  x  =  y  ->  ph )
31, 2syl 14 1  |-  ( -. 
A. x  x  =  y  ->  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1361
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-fal 1369
This theorem is referenced by:  sbal2  2030
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