Theorem hbnaes 1701

Description: Rule that applies hbnae 1699 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

Step	Hyp	Ref	Expression
1		hbnae 1699	. 2 |- ( -. A. x x = y -> A. z -. A. x x = y )
2		hbnalequs.1	. 2 |- ( A. z -. A. x x = y -> ph )
3	1, 2	syl 14	1 |- ( -. A. x x = y -> ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1329

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337

This theorem is referenced by:  sbal2  1997