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Mirrors > Home > ILE Home > Th. List > expi | GIF version |
Description: An exportation inference. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 28-Nov-2008.) |
Ref | Expression |
---|---|
expi.1 | ⊢ (¬ (𝜑 → ¬ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
expi | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.2im 632 | . 2 ⊢ (𝜑 → (𝜓 → ¬ (𝜑 → ¬ 𝜓))) | |
2 | expi.1 | . 2 ⊢ (¬ (𝜑 → ¬ 𝜓) → 𝜒) | |
3 | 1, 2 | syl6 33 | 1 ⊢ (𝜑 → (𝜓 → 𝜒)) |
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-nn0suc0 13950 |
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