Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > mp3an12i | GIF version |
Description: mp3an 1319 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 1309 | . 2 ⊢ (𝜃 → 𝜏) |
6 | 1, 5 | syl 14 | 1 ⊢ (𝜒 → 𝜏) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 963 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 965 |
This theorem is referenced by: map1 6757 suplocsrlempr 7727 geo2lim 11413 fprodge0 11534 fprodge1 11536 oddp1d2 11780 bezoutlema 11882 bezoutlemb 11883 exmidunben 12155 ismet 12744 isxmet 12745 coseq0negpitopi 13157 cosq34lt1 13171 cos02pilt1 13172 logdivlti 13202 |
Copyright terms: Public domain | W3C validator |