Theorem hbaes 1699

Description: Rule that applies hbae 1697 to antecedent. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
hbalequs.1	|- ( A. z A. x x = y -> ph )

Assertion

Ref	Expression
hbaes	|- ( A. x x = y -> ph )

Proof of Theorem hbaes

Step	Hyp	Ref	Expression
1		hbae 1697	. 2 |- ( A. x x = y -> A. z A. x x = y )
2		hbalequs.1	. 2 |- ( A. z A. x x = y -> ph )
3	1, 2	syl 14	1 |- ( A. x x = y -> ph )

Syntax hints:   -> wi 4   A.wal 1330

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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)