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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-con2com | Structured version Visualization version GIF version |
Description: A commuted form of the contrapositive, true in minimal calculus. (Contributed by BJ, 19-Mar-2020.) |
Ref | Expression |
---|---|
bj-con2com | ⊢ (𝜑 → ((𝜓 → ¬ 𝜑) → ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con2 135 | . 2 ⊢ ((𝜓 → ¬ 𝜑) → (𝜑 → ¬ 𝜓)) | |
2 | 1 | com12 32 | 1 ⊢ (𝜑 → ((𝜓 → ¬ 𝜑) → ¬ 𝜓)) |
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-con2comi 34738 |
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