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Mirrors > Home > ILE Home > Th. List > exp516 | GIF version |
Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009.) |
Ref | Expression |
---|---|
exp516.1 | ⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) ∧ 𝜏) → 𝜂) |
Ref | Expression |
---|---|
exp516 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp516.1 | . . 3 ⊢ (((𝜑 ∧ (𝜓 ∧ 𝜒 ∧ 𝜃)) ∧ 𝜏) → 𝜂) | |
2 | 1 | exp31 364 | . 2 ⊢ (𝜑 → ((𝜓 ∧ 𝜒 ∧ 𝜃) → (𝜏 → 𝜂))) |
3 | 2 | 3expd 1225 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → (𝜏 → 𝜂))))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 ∧ w3a 979 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 df-3an 981 |
This theorem is referenced by: (None) |
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