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Mirrors > Home > NFE 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 137 | . . 3 ⊢ (φ → (ψ → ¬ (φ → ¬ ψ))) | |
2 | 1 | imim1d 69 | . 2 ⊢ (φ → ((¬ (φ → ¬ ψ) → χ) → (ψ → χ))) |
3 | 2 | com12 27 | 1 ⊢ ((¬ (φ → ¬ ψ) → χ) → (φ → (ψ → χ))) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem is referenced by: (None) |
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