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Theorem bj-nimn 31143
Description: If a formula is true, then it does not imply its negation. (Contributed by BJ, 19-Mar-2020.) A shorter proof is possible using id 22 and jc 150, however, the present proof uses theorems that are more basic than jc 150. (Proof modification is discouraged.)
Assertion
Ref Expression
bj-nimn  |-  ( ph  ->  -.  ( ph  ->  -. 
ph ) )

Proof of Theorem bj-nimn
StepHypRef Expression
1 pm2.01 171 . 2  |-  ( (
ph  ->  -.  ph )  ->  -.  ph )
21con2i 123 1  |-  ( ph  ->  -.  ( ph  ->  -. 
ph ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  bj-nimni  31144
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