Theorem hbnaes 1734

Description: Rule that applies hbnae 1732 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 1732	. 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 1362

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 1458  ax-7 1459  ax-gen 1460  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370

This theorem is referenced by:  sbal2  2032