Theorem imanim 823

Description: Express implication in terms of conjunction. The converse only holds given a decidability condition; see imandc 824. (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 820	. 2 |- ( ( ph /\ -. ps ) -> -. ( ph -> ps ) )
2	1	con2i 592	1 |- ( ( ph -> ps ) -> -. ( ph /\ -. ps ) )

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

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-in1 579  ax-in2 580

This theorem is referenced by:  difdif  3125  ssdif0im  3347  inssdif0im  3350  nominpos  8651