Theorem niabn 874

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 103	. 2 |- ( ( ch /\ ps ) -> ps )
2		niabn.1	. . 3 |- ph
3	2	pm2.24i 553	. 2 |- ( -. ph -> ps )
4	1, 3	pm5.21ni 619	1 |- ( -. ps -> ( ( ch /\ ps ) <-> -. ph ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 97   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  ninba  879