Theorem ninba 927

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

Hypothesis

Ref	Expression
ninba.1	|- ph

Assertion

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

Proof of Theorem ninba

Step	Hyp	Ref	Expression
1		ninba.1	. . 3 |- ph
2	1	niabn 917	. 2 |- (-. ps -> ((ch /\ ps) <-> -. ph))
3	2	bicomd 192	1 |- (-. ps -> (-. ph <-> (ch /\ ps)))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is referenced by: (None)