Theorem hbnaes 2319

Description: Rule that applies hbnae 2317 to antecedent. (Contributed by NM, 15-May-1993.)

Hypothesis

Ref	Expression
hbnaes.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 2317	. 2 |- ( -. A. x x = y -> A. z -. A. x x = y )
2		hbnaes.1	. 2 |- ( A. z -. A. x x = y -> ph )
3	1, 2	syl 17	1 |- ( -. A. x x = y -> ph )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)