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Mirrors > Home > ILE Home > Th. List > con3rr3 | GIF version |
Description: Rotate through consequent right. (Contributed by Wolf Lammen, 3-Nov-2013.) |
Ref | Expression |
---|---|
con3rr3.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
con3rr3 | ⊢ (¬ 𝜒 → (𝜑 → ¬ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | con3rr3.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | 1 | con3d 621 | . 2 ⊢ (𝜑 → (¬ 𝜒 → ¬ 𝜓)) |
3 | 2 | com12 30 | 1 ⊢ (¬ 𝜒 → (𝜑 → ¬ 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 604 ax-in2 605 |
This theorem is referenced by: imnan 680 snnen2og 6805 bj-nnim 13353 |
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