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Mirrors > Home > MPE Home > Th. List > imim12 | Structured version Visualization version GIF version |
Description: Closed form of imim12i 62 and of 3syl 18. (Contributed by BJ, 16-Jul-2019.) |
Ref | Expression |
---|---|
imim12 | ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜃) → ((𝜓 → 𝜒) → (𝜑 → 𝜃)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imim2 58 | . . . 4 ⊢ ((𝜒 → 𝜃) → ((𝜓 → 𝜒) → (𝜓 → 𝜃))) | |
2 | 1 | com13 88 | . . 3 ⊢ (𝜓 → ((𝜓 → 𝜒) → ((𝜒 → 𝜃) → 𝜃))) |
3 | 2 | imim2i 16 | . 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → ((𝜓 → 𝜒) → ((𝜒 → 𝜃) → 𝜃)))) |
4 | 3 | com24 95 | 1 ⊢ ((𝜑 → 𝜓) → ((𝜒 → 𝜃) → ((𝜓 → 𝜒) → (𝜑 → 𝜃)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: (None) |
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