Theorem hbn1 1017

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 1005	. 2 |- (A.xph -> A.xA.xph)
2	1	hbn 1006	1 |- (-. A.xph -> A.x -. A.xph)

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

This theorem is referenced by:  hbe1 1018  ax467 1025  modal-5 1029  equs4 1152  equs5e 1200  ax15 1361  ax11indn 1368  a12lem1 1378  a12study 1380  a12studyALT 1381

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-4 975  ax-5o 977  ax-6o 980

Copyright terms: Public domain