Theorem imanim 785

Description: Express implication in terms of conjunction. The converse only holds given a decidability condition; see imandc 786. (Contributed by Jim Kingdon, 24-Dec-2017.)

Assertion

Ref	Expression
imanim	|- ( ( ph -> ps ) -> -. ( ph /\ -. ps ) )

Proof of Theorem imanim

Step	Hyp	Ref	Expression
1		annimim 782	. 2 |- ( ( ph /\ -. ps ) -> -. ( ph -> ps ) )
2	1	con2i 557	1 |- ( ( ph -> ps ) -> -. ( ph /\ -. ps ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-in1 544  ax-in2 545

This theorem is referenced by:  difdif  3069  npss0  3266  ssdif0im  3286  inssdif0im  3291  nominpos  8162