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Mirrors > Home > MPE Home > Th. List > Mathboxes > e33an | Structured version Visualization version GIF version |
Description: Conjunction form of e33 42324. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
e33an.1 | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) |
e33an.2 | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜏 ) |
e33an.3 | ⊢ ((𝜃 ∧ 𝜏) → 𝜂) |
Ref | Expression |
---|---|
e33an | ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜂 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | e33an.1 | . 2 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜃 ) | |
2 | e33an.2 | . 2 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜏 ) | |
3 | e33an.3 | . . 3 ⊢ ((𝜃 ∧ 𝜏) → 𝜂) | |
4 | 3 | ex 413 | . 2 ⊢ (𝜃 → (𝜏 → 𝜂)) |
5 | 1, 2, 4 | e33 42324 | 1 ⊢ ( 𝜑 , 𝜓 , 𝜒 ▶ 𝜂 ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 ( wvd3 42177 |
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 397 df-3an 1088 df-vd3 42180 |
This theorem is referenced by: (None) |
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