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Mirrors > Home > ILE Home > Th. List > imp4a | GIF version |
Description: An importation inference. (Contributed by NM, 26-Apr-1994.) |
Ref | Expression |
---|---|
imp4.1 | ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) |
Ref | Expression |
---|---|
imp4a | ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imp4.1 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 → (𝜃 → 𝜏)))) | |
2 | impexp 250 | . 2 ⊢ (((𝜒 ∧ 𝜃) → 𝜏) ↔ (𝜒 → (𝜃 → 𝜏))) | |
3 | 1, 2 | syl6ibr 151 | 1 ⊢ (𝜑 → (𝜓 → ((𝜒 ∧ 𝜃) → 𝜏))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: imp4b 332 imp4d 334 imp55 343 imp511 344 equs5or 1711 reuss2 3217 tfrlem9 5935 |
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