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Mirrors > Home > ILE Home > Th. List > ancl | GIF version |
Description: Conjoin antecedent to left of consequent. (Contributed by NM, 15-Aug-1994.) |
Ref | Expression |
---|---|
ancl | ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜑 ∧ 𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.2 138 | . 2 ⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜓))) | |
2 | 1 | a2i 11 | 1 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜑 ∧ 𝜓))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 |
This theorem was proved from axioms: ax-mp 5 ax-2 7 ax-ia3 107 |
This theorem is referenced by: equs4 1705 eupickbi 2088 |
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