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Mirrors > Home > MPE Home > Th. List > Mathboxes > eel0321old | Structured version Visualization version GIF version |
Description: el0321old 37963 without virtual deductions. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
eel0321old.1 | ⊢ 𝜑 |
eel0321old.2 | ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏) |
eel0321old.3 | ⊢ ((𝜑 ∧ 𝜏) → 𝜂) |
Ref | Expression |
---|---|
eel0321old | ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜂) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eel0321old.1 | . 2 ⊢ 𝜑 | |
2 | eel0321old.2 | . 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜏) | |
3 | eel0321old.3 | . 2 ⊢ ((𝜑 ∧ 𝜏) → 𝜂) | |
4 | 1, 2, 3 | sylancr 694 | 1 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜃) → 𝜂) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 ∧ w3a 1031 |
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: el0321old 37963 suctrALTcf 38180 |
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