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Mirrors > Home > ILE Home > Th. List > exp41 | GIF version |
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.) |
Ref | Expression |
---|---|
exp41.1 | ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏) |
Ref | Expression |
---|---|
exp41 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exp41.1 | . . 3 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) → 𝜏) | |
2 | 1 | ex 112 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → (𝜃 → 𝜏)) |
3 | 2 | exp31 350 | 1 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 101 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia3 105 |
This theorem is referenced by: (None) |
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