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Mathbox for Alan Sare |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > eel000cT | Structured version Visualization version GIF version |
Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
eel000cT.1 | ⊢ 𝜑 |
eel000cT.2 | ⊢ 𝜓 |
eel000cT.3 | ⊢ 𝜒 |
eel000cT.4 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
eel000cT | ⊢ (⊤ → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eel000cT.3 | . . 3 ⊢ 𝜒 | |
2 | eel000cT.2 | . . . 4 ⊢ 𝜓 | |
3 | eel000cT.1 | . . . . 5 ⊢ 𝜑 | |
4 | eel000cT.4 | . . . . 5 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
5 | 3, 4 | mp3an1 1403 | . . . 4 ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
6 | 2, 5 | mpan 702 | . . 3 ⊢ (𝜒 → 𝜃) |
7 | 1, 6 | ax-mp 5 | . 2 ⊢ 𝜃 |
8 | 7 | a1i 11 | 1 ⊢ (⊤ → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1031 ⊤wtru 1476 |
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-3an 1033 |
This theorem is referenced by: (None) |
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