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Mathbox for Alan Sare |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > e01an | Structured version Visualization version GIF version |
Description: Conjunction form of e01 37937. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e01an.1 | ⊢ 𝜑 |
e01an.2 | ⊢ ( 𝜓 ▶ 𝜒 ) |
e01an.3 | ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
e01an | ⊢ ( 𝜓 ▶ 𝜃 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e01an.1 | . 2 ⊢ 𝜑 | |
2 | e01an.2 | . 2 ⊢ ( 𝜓 ▶ 𝜒 ) | |
3 | e01an.3 | . . 3 ⊢ ((𝜑 ∧ 𝜒) → 𝜃) | |
4 | 3 | ex 449 | . 2 ⊢ (𝜑 → (𝜒 → 𝜃)) |
5 | 1, 2, 4 | e01 37937 | 1 ⊢ ( 𝜓 ▶ 𝜃 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ( wvd1 37806 |
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 196 df-an 385 df-vd1 37807 |
This theorem is referenced by: unipwrVD 38089 |
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