Theorem bianfi 947

Description: A wff conjoined with falsehood is false. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 26-Nov-2012.)

Hypothesis

Ref	Expression
bianfi.1	|- -. ph

Assertion

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

Proof of Theorem bianfi

Step	Hyp	Ref	Expression
1		bianfi.1	. 2 |- -. ph
2	1	intnan 929	. 2 |- -. ( ps /\ ph )
3	1, 2	2false 701	1 |- ( ph <-> ( ps /\ ph ) )

Syntax hints:   -. wn 3   /\ wa 104   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  in0  3459  opthprc  4679