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Theorem imanim 662
Description: Express implication in terms of conjunction. The converse only holds given a decidability condition; see imandc 859. (Contributed by Jim Kingdon, 24-Dec-2017.)
Assertion
Ref Expression
imanim  |-  ( (
ph  ->  ps )  ->  -.  ( ph  /\  -.  ps ) )

Proof of Theorem imanim
StepHypRef Expression
1 annimim 660 . 2  |-  ( (
ph  /\  -.  ps )  ->  -.  ( ph  ->  ps ) )
21con2i 601 1  |-  ( (
ph  ->  ps )  ->  -.  ( ph  /\  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-in1 588  ax-in2 589
This theorem is referenced by:  difdif  3171  ssdif0im  3397  inssdif0im  3400  nominpos  8925
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