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Mirrors > Home > MPE Home > Th. List > Mathboxes > ee10an | Structured version Visualization version GIF version |
Description: e10an 42268 without virtual deductions. sylancl 585 is also e10an 42268 without virtual deductions, except the order of the hypotheses is different. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ee10an.1 | ⊢ (𝜑 → 𝜓) |
ee10an.2 | ⊢ 𝜒 |
ee10an.3 | ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
ee10an | ⊢ (𝜑 → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee10an.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | ee10an.2 | . 2 ⊢ 𝜒 | |
3 | ee10an.3 | . 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜃) | |
4 | 1, 2, 3 | sylancl 585 | 1 ⊢ (𝜑 → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 395 |
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 396 |
This theorem is referenced by: (None) |
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