Theorem hbnaes 1148

Description: Rule that applies hbnae 1147 to antecedent.

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 1147	. 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 10	1 |- (-. A.x x = y -> ph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 954   = wceq 956

This theorem is referenced by:  sb9i 1263  sbal1 1346  sbal2 1358  ralcom2 1776

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-10 966  ax-12 968  ax-4 973  ax-5o 975  ax-6o 978  ax-10o 1140

Copyright terms: Public domain