Theorem bianfd 938

Description: A wff conjoined with falsehood is false. (Contributed by NM, 27-Mar-1995.) (Proof shortened by Wolf Lammen, 5-Nov-2013.)

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	. 2 |- ( ph -> -. ps )
2	1	intnanrd 922	. 2 |- ( ph -> -. ( ps /\ ch ) )
3	1, 2	2falsed 692	1 |- ( ph -> ( ps <-> ( ps /\ ch ) ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 103   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  eueq2dc  2899  eueq3dc  2900