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Mirrors > Home > MPE Home > Th. List > 3imp31 | Structured version Visualization version GIF version |
Description: The importation inference 3imp 1112 with commutation of the first and third conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016.) |
Ref | Expression |
---|---|
3imp.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
Ref | Expression |
---|---|
3imp31 | ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3imp.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | 1 | com13 88 | . 2 ⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃))) |
3 | 2 | 3imp 1112 | 1 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1088 |
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 206 df-an 398 df-3an 1090 |
This theorem is referenced by: 3com13 1125 dvdsmodexp 16152 gsummatr01lem4 22030 elntg2 27983 pthdadjvtx 28727 umgr2cwwk2dif 29057 frgrwopreglem2 29306 relexpxpmin 42081 prproropf1olem4 45788 resum2sqorgt0 46885 |
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