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Mirrors > Home > MPE Home > Th. List > Mathboxes > eel021old | Structured version Visualization version GIF version |
Description: el021old 37947 without virtual deductions. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
eel021.1 | ⊢ 𝜑 |
eel021.2 | ⊢ ((𝜓 ∧ 𝜒) → 𝜃) |
eel021.3 | ⊢ ((𝜑 ∧ 𝜃) → 𝜏) |
Ref | Expression |
---|---|
eel021old | ⊢ ((𝜓 ∧ 𝜒) → 𝜏) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eel021.1 | . 2 ⊢ 𝜑 | |
2 | eel021.2 | . 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜃) | |
3 | eel021.3 | . 2 ⊢ ((𝜑 ∧ 𝜃) → 𝜏) | |
4 | 1, 2, 3 | sylancr 694 | 1 ⊢ ((𝜓 ∧ 𝜒) → 𝜏) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
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 |
This theorem is referenced by: sspwimpcf 38178 suctrALTcf 38180 |
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