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Theorem imanim 819
Description: Express implication in terms of conjunction. The converse only holds given a decidability condition; see imandc 820. (Contributed by Jim Kingdon, 24-Dec-2017.)
Assertion
Ref Expression
imanim  |-  ( (
ph  ->  ps )  ->  -.  ( ph  /\  -.  ps ) )

Proof of Theorem imanim
StepHypRef Expression
1 annimim 816 . 2  |-  ( (
ph  /\  -.  ps )  ->  -.  ( ph  ->  ps ) )
21con2i 590 1  |-  ( (
ph  ->  ps )  ->  -.  ( ph  /\  -.  ps ) )
Colors of variables: wff set class
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 577  ax-in2 578
This theorem is referenced by:  difdif  3098  ssdif0im  3315  inssdif0im  3318  nominpos  8335
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