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Mirrors > Home > MPE Home > Th. List > pm2.61ii | Structured version Visualization version GIF version |
Description: Inference eliminating two antecedents. (Contributed by NM, 4-Jan-1993.) (Proof shortened by Josh Purinton, 29-Dec-2000.) |
Ref | Expression |
---|---|
pm2.61ii.1 | ⊢ (¬ 𝜑 → (¬ 𝜓 → 𝜒)) |
pm2.61ii.2 | ⊢ (𝜑 → 𝜒) |
pm2.61ii.3 | ⊢ (𝜓 → 𝜒) |
Ref | Expression |
---|---|
pm2.61ii | ⊢ 𝜒 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.61ii.2 | . 2 ⊢ (𝜑 → 𝜒) | |
2 | pm2.61ii.1 | . . 3 ⊢ (¬ 𝜑 → (¬ 𝜓 → 𝜒)) | |
3 | pm2.61ii.3 | . . 3 ⊢ (𝜓 → 𝜒) | |
4 | 2, 3 | pm2.61d2 172 | . 2 ⊢ (¬ 𝜑 → 𝜒) |
5 | 1, 4 | pm2.61i 176 | 1 ⊢ 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: pm2.61iii 179 hbae 2457 pssnn 8343 alephadd 9591 axextnd 9605 axunnd 9610 axpownd 9615 axregndlem2 9617 axregnd 9618 axinfndlem1 9619 axinfnd 9620 2cshwcshw 13771 ressress 16140 frgrreg 27562 bj-hbaeb2 33111 hbae-o 34692 hbequid 34698 ax5eq 34721 ax5el 34726 odd2prm2 42137 |
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