Theorem hbn1 708

Description: x is not free in -. A.xph.

Assertion

Ref	Expression
hbn1	|- (-. A.xph -> A.x -. A.xph)

Proof of Theorem hbn1

Step	Hyp	Ref	Expression
1		hba1 698	. 2 |- (A.xph -> A.xA.xph)
2	1	hbne 699	1 |- (-. A.xph -> A.x -. A.xph)

Syntax hints:  -. wn 1   -> wi 2  A.wal 672

This theorem is referenced by:  hbe1 709  ax6 711  eqs1 828  eqs2 829  ax15 1006

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677

metamath.org