Theorem niabn 969

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 110	. 2 |- ( ( ch /\ ps ) -> ps )
2		niabn.1	. . 3 |- ph
3	2	pm2.24i 624	. 2 |- ( -. ph -> ps )
4	1, 3	pm5.21ni 704	1 |- ( -. ps -> ( ( ch /\ ps ) <-> -. ph ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  ninba  974