Theorem nan 658

Description: Theorem to move a conjunct in and out of a negation. (Contributed by NM, 9-Nov-2003.)

Assertion

Ref	Expression
nan	|- ( ( ph -> -. ( ps /\ ch ) ) <-> ( ( ph /\ ps ) -> -. ch ) )

Proof of Theorem nan

Step	Hyp	Ref	Expression
1		impexp 259	. 2 |- ( ( ( ph /\ ps ) -> -. ch ) <-> ( ph -> ( ps -> -. ch ) ) )
2		imnan 656	. . 3 |- ( ( ps -> -. ch ) <-> -. ( ps /\ ch ) )
3	2	imbi2i 224	. 2 |- ( ( ph -> ( ps -> -. ch ) ) <-> ( ph -> -. ( ps /\ ch ) ) )
4	1, 3	bitr2i 183	1 |- ( ( ph -> -. ( ps /\ ch ) ) <-> ( ( ph /\ ps ) -> -. ch ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 102   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  pm4.15  822