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Mirrors > Home > ILE Home > Th. List > impac | GIF version |
Description: Importation with conjunction in consequent. (Contributed by NM, 9-Aug-1994.) |
Ref | Expression |
---|---|
impac.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
impac | ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | impac.1 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
2 | 1 | ancrd 319 | . 2 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜓))) |
3 | 2 | imp 122 | 1 ⊢ ((𝜑 ∧ 𝜓) → (𝜒 ∧ 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 102 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem is referenced by: imdistanri 434 f1elima 5433 |
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