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Mirrors > Home > MPE Home > Th. List > Mathboxes > ee30an | Structured version Visualization version GIF version |
Description: Conjunction form of ee30 42067. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
ee30an.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) |
ee30an.2 | ⊢ 𝜏 |
ee30an.3 | ⊢ ((𝜃 ∧ 𝜏) → 𝜂) |
Ref | Expression |
---|---|
ee30an | ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ee30an.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜃))) | |
2 | ee30an.2 | . 2 ⊢ 𝜏 | |
3 | ee30an.3 | . . 3 ⊢ ((𝜃 ∧ 𝜏) → 𝜂) | |
4 | 3 | ex 416 | . 2 ⊢ (𝜃 → (𝜏 → 𝜂)) |
5 | 1, 2, 4 | ee30 42067 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → 𝜂))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 |
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 210 df-an 400 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |