Theorem bianfd 554

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 74	. 2 |- (ph -> (ps -> (ps /\ ch)))
3		pm3.26 256	. . 3 |- ((ps /\ ch) -> ps)
4	3	a1i 7	. 2 |- (ph -> ((ps /\ ch) -> ps))
5	2, 4	impbid 397	1 |- (ph -> (ps <-> (ps /\ ch)))

Syntax hints:  -. wn 1   -> wi 2   <-> wb 127   /\ wa 196

This theorem is referenced by:  eueq2 1429  eueq3 1430

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

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org