Theorem niabn 758

Description: Miscellaneous inference relating falsehoods.

Hypothesis

Ref	Expression
niabn.1	|- ph

Assertion

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

Proof of Theorem niabn

Step	Hyp	Ref	Expression
1		pm3.27 323	. 2 |- ((ch /\ ps) -> ps)
2		niabn.1	. . 3 |- ph
3	2	pm2.24i 104	. 2 |- (-. ph -> ps)
4	1, 3	pm5.21ni 677	1 |- (-. ps -> ((ch /\ ps) <-> -. ph))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   /\ wa 223

This theorem is referenced by:  ninba 768

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

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