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Mirrors > Home > MPE Home > Th. List > Mathboxes > ee11an | Structured version Visualization version GIF version |
Description: e11an 41982 without virtual deductions. syl22anc 839 is also e11an 41982 without virtual deductions, exept with a different order of hypotheses. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ee11an.1 | ⊢ (𝜑 → 𝜓) |
ee11an.2 | ⊢ (𝜑 → 𝜒) |
ee11an.3 | ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
ee11an | ⊢ (𝜑 → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee11an.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | ee11an.2 | . 2 ⊢ (𝜑 → 𝜒) | |
3 | ee11an.3 | . . 3 ⊢ ((𝜓 ∧ 𝜒) → 𝜃) | |
4 | 3 | ex 416 | . 2 ⊢ (𝜓 → (𝜒 → 𝜃)) |
5 | 1, 2, 4 | sylc 65 | 1 ⊢ (𝜑 → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 |
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 210 df-an 400 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |