Theorem bianfi 739

Description: A wff conjoined with falsehood is false.

Hypothesis

Ref	Expression
bianfi.1	|- -. ph

Assertion

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

Proof of Theorem bianfi

Step	Hyp	Ref	Expression
1		bianfi.1	. . 3 |- -. ph
2	1	pm2.21i 77	. 2 |- (ph -> (ps /\ ph))
3		pm3.27 323	. 2 |- ((ps /\ ph) -> ph)
4	2, 3	impbi 157	1 |- (ph <-> (ps /\ ph))

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

This theorem is referenced by:  in0 2302  opthprc 3227

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