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Mirrors > Home > ILE Home > Th. List > ancr | GIF version |
Description: Conjoin antecedent to right of consequent. (Contributed by NM, 15-Aug-1994.) |
Ref | Expression |
---|---|
ancr | ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜓 ∧ 𝜑))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.21 260 | . 2 ⊢ (𝜑 → (𝜓 → (𝜓 ∧ 𝜑))) | |
2 | 1 | a2i 11 | 1 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜓 ∧ 𝜑))) |
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-ia3 106 |
This theorem is referenced by: bimsc1 904 ssddif 3198 reupick2 3250 intmin4 3664 |
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