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Mirrors > Home > ILE Home > Th. List > 3imp31 | GIF version |
Description: The importation inference 3imp 1188 with commutation of the first and third conjuncts of the assertion relative to the hypothesis. (Contributed by Alan Sare, 11-Sep-2016.) |
Ref | Expression |
---|---|
3imp31.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
Ref | Expression |
---|---|
3imp31 | ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3imp31.1 | . . 3 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | 1 | com13 80 | . 2 ⊢ (𝜒 → (𝜓 → (𝜑 → 𝜃))) |
3 | 2 | 3imp 1188 | 1 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 973 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 |
This theorem depends on definitions: df-bi 116 df-3an 975 |
This theorem is referenced by: dvdsmodexp 11744 |
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