Theorem hbn1 1013

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 1001	. 2 |- (A.xph -> A.xA.xph)
2	1	hbn 1002	1 |- (-. A.xph -> A.x -. A.xph)

Syntax hints:  -. wn 2   -> wi 3  A.wal 952

This theorem is referenced by:  hbe1 1014  ax467 1021  modal-5 1025  equs4 1148  equs5e 1196  ax15 1357  ax11indn 1364  a12lem1 1374  a12study 1376  a12studyALT 1377

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-4 971  ax-5o 973  ax-6o 976

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