Description: Conjoin antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994)
Ref | Expression | ||
---|---|---|---|
Assertion | anc2r | ⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜑 → ( 𝜓 → ( 𝜒 ∧ 𝜑 ) ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.21 | ⊢ ( 𝜑 → ( 𝜒 → ( 𝜒 ∧ 𝜑 ) ) ) | |
2 | 1 | imim2d | ⊢ ( 𝜑 → ( ( 𝜓 → 𝜒 ) → ( 𝜓 → ( 𝜒 ∧ 𝜑 ) ) ) ) |
3 | 2 | a2i | ⊢ ( ( 𝜑 → ( 𝜓 → 𝜒 ) ) → ( 𝜑 → ( 𝜓 → ( 𝜒 ∧ 𝜑 ) ) ) ) |