Theorem bianfd 738

Description: A wff conjoined with falsehood is false.

Hypothesis

Ref	Expression
bianfd.1	|- (ph -> -. ps)

Assertion

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

Proof of Theorem bianfd

Step	Hyp	Ref	Expression
1		bianfd.1	. . 3 |- (ph -> -. ps)
2	1	pm2.21d 78	. 2 |- (ph -> (ps -> (ps /\ ch)))
3		pm3.26 319	. 2 |- ((ps /\ ch) -> ps)
4	2, 3	impbid1 517	1 |- (ph -> (ps <-> (ps /\ ch)))

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

This theorem is referenced by:  eueq2 1918  eueq3 1919

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

Copyright terms: Public domain