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Theorem bj-imnimnn 13738
Description: If a formula is implied by both a formula and its negation, then it is not refutable. There is another proof using the inference associated with bj-nnclavius 13737 as its last step. (Contributed by BJ, 27-Oct-2024.)
Hypotheses
Ref Expression
bj-imnimnn.1 (𝜑𝜓)
bj-imnimnn.2 𝜑𝜓)
Assertion
Ref Expression
bj-imnimnn ¬ ¬ 𝜓

Proof of Theorem bj-imnimnn
StepHypRef Expression
1 bj-imnimnn.1 . . 3 (𝜑𝜓)
21con3i 627 . 2 𝜓 → ¬ 𝜑)
3 bj-imnimnn.2 . . 3 𝜑𝜓)
43con3i 627 . 2 𝜓 → ¬ ¬ 𝜑)
52, 4pm2.65i 634 1 ¬ ¬ 𝜓
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 609  ax-in2 610
This theorem is referenced by:  bj-nnst  13743
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