Theorem niabn 917

Description: Miscellaneous inference relating falsehoods. (Contributed by NM, 31-Mar-1994.)

Hypothesis

Ref	Expression
niabn.1	|- ph

Assertion

Ref	Expression
niabn	|- (-. ps -> ((ch /\ ps) <-> -. ph))

Proof of Theorem niabn

Step	Hyp	Ref	Expression
1		simpr 447	. 2 |- ((ch /\ ps) -> ps)
2		niabn.1	. . 3 |- ph
3	2	pm2.24i 136	. 2 |- (-. ph -> ps)
4	1, 3	pm5.21ni 341	1 |- (-. ps -> ((ch /\ ps) <-> -. ph))

This proof depends on syntax axioms:  -. wn 3   -> wi 4   <-> wb 176   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  ninba  927