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Mirrors > Home > MPE Home > Th. List > mp3an12i | Structured version Visualization version GIF version |
Description: mp3an 1416 with antecedents in standard conjunction form and with one hypothesis an implication. (Contributed by Alan Sare, 28-Aug-2016.) |
Ref | Expression |
---|---|
mp3an12i.1 | ⊢ 𝜑 |
mp3an12i.2 | ⊢ 𝜓 |
mp3an12i.3 | ⊢ (𝜒 → 𝜃) |
mp3an12i.4 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜏) |
Ref | Expression |
---|---|
mp3an12i | ⊢ (𝜒 → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mp3an12i.3 | . 2 ⊢ (𝜒 → 𝜃) | |
2 | mp3an12i.1 | . . 3 ⊢ 𝜑 | |
3 | mp3an12i.2 | . . 3 ⊢ 𝜓 | |
4 | mp3an12i.4 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜃) → 𝜏) | |
5 | 2, 3, 4 | mp3an12 1406 | . 2 ⊢ (𝜃 → 𝜏) |
6 | 1, 5 | syl 17 | 1 ⊢ (𝜒 → 𝜏) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1031 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-an 385 df-3an 1033 |
This theorem is referenced by: ener 7888 hashfun 13084 funcnvs2 13508 3dvds 14890 oddp1d2 14920 bitsres 15033 bposlem9 24817 gausslemma2dlem1 24891 poimirlem26 32605 mblfinlem2 32617 isosctrlem1ALT 38192 fmtnorec1 39987 evengpoap3 40215 umgr2v2e 40741 0wlkOnlem2 41287 |
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