Theorem hbnaes 1508

Description: Rule that applies hbnae 1507 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 1507	. 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 12	1 |- (-. A.x x = y -> ph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 1296   = wceq 1298

This theorem is referenced by:  sb9i 1640  sbal1 1737  sbal2 1749  ralcom2OLD 2245

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-10 1308  ax-12 1310  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-10o 1500

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