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Mirrors > Home > NFE Home > Th. List > pm2.61d1 | GIF version |
Description: Inference eliminating an antecedent. (Contributed by NM, 15-Jul-2005.) |
Ref | Expression |
---|---|
pm2.61d1.1 | ⊢ (φ → (ψ → χ)) |
pm2.61d1.2 | ⊢ (¬ ψ → χ) |
Ref | Expression |
---|---|
pm2.61d1 | ⊢ (φ → χ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.61d1.1 | . 2 ⊢ (φ → (ψ → χ)) | |
2 | pm2.61d1.2 | . . 3 ⊢ (¬ ψ → χ) | |
3 | 2 | a1i 10 | . 2 ⊢ (φ → (¬ ψ → χ)) |
4 | 1, 3 | pm2.61d 150 | 1 ⊢ (φ → χ) |
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: ja 153 pm2.61nii 158 pm2.01d 161 ax10lem2 1937 mo 2226 2mo 2282 mosubopt 4612 funfv 5375 fvmptnf 5723 |
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