Theorem bianfi 553

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 73	. 2 |- (ph -> (ps /\ ph))
3		pm3.27 260	. 2 |- ((ps /\ ph) -> ph)
4	2, 3	impbi 139	1 |- (ph <-> (ps /\ ph))

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

This theorem is referenced by:  in0 1722  opthprc 2457

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

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