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Mirrors > Home > ILE Home > Th. List > expt | GIF version |
Description: Exportation theorem expressed with primitive connectives. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
expt | ⊢ ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (𝜑 → (𝜓 → 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.2im 576 | . . 3 ⊢ (𝜑 → (𝜓 → ¬ (𝜑 → ¬ 𝜓))) | |
2 | 1 | imim1d 73 | . 2 ⊢ (𝜑 → ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (𝜓 → 𝜒))) |
3 | 2 | com12 30 | 1 ⊢ ((¬ (𝜑 → ¬ 𝜓) → 𝜒) → (𝜑 → (𝜓 → 𝜒))) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-in1 554 ax-in2 555 |
This theorem is referenced by: (None) |
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