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Mirrors > Home > ILE Home > Th. List > exp520 | GIF version |
Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.) |
Ref | Expression |
---|---|
exp520.1 | ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ (𝜃 ∧ 𝜏)) → 𝜂) |
Ref | Expression |
---|---|
exp520 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp520.1 | . . 3 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ (𝜃 ∧ 𝜏)) → 𝜂) | |
2 | 1 | ex 114 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → ((𝜃 ∧ 𝜏) → 𝜂)) |
3 | 2 | exp5o 1208 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ∧ w3a 963 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 965 |
This theorem is referenced by: (None) |
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