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Mirrors > Home > ILE Home > Th. List > impancom | GIF version |
Description: Mixed importation/commutation inference. (Contributed by NM, 22-Jun-2013.) |
Ref | Expression |
---|---|
impancom.1 | ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) |
Ref | Expression |
---|---|
impancom | ⊢ ((𝜑 ∧ 𝜒) → (𝜓 → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | impancom.1 | . . . 4 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 → 𝜃)) | |
2 | 1 | ex 115 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
3 | 2 | com23 78 | . 2 ⊢ (𝜑 → (𝜒 → (𝜓 → 𝜃))) |
4 | 3 | imp 124 | 1 ⊢ ((𝜑 ∧ 𝜒) → (𝜓 → 𝜃)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem is referenced by: eqrdav 2188 disjiun 4013 euotd 4269 onsucelsucr 4522 isotr 5833 spc2ed 6252 ltbtwnnqq 7432 genpcdl 7536 genpcuu 7537 un0addcl 9227 un0mulcl 9228 btwnnz 9365 uznfz 10121 elfz0ubfz0 10143 fzoss1 10189 elfzo0z 10202 fzofzim 10206 elfzom1p1elfzo 10232 ssfzo12bi 10243 subfzo0 10260 modfzo0difsn 10413 expaddzap 10582 caucvgre 11008 caubnd2 11144 summodc 11409 fzo0dvdseq 11881 nno 11929 lcmdvds 12097 hashgcdeq 12257 modprm0 12272 pcqcl 12324 issubg4m 13098 01eq0ring 13497 neii1 14044 neii2 14046 fsumcncntop 14453 |
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