Theorem anc2r 564

Description: Conjoin antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994.)

Assertion

Ref	Expression
anc2r	⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → (𝜒 ∧ 𝜑))))

Proof of Theorem anc2r

Step	Hyp	Ref	Expression
1		pm3.21 477	. . 3 ⊢ (𝜑 → (𝜒 → (𝜒 ∧ 𝜑)))
2	1	imim2d 58	. 2 ⊢ (𝜑 → ((𝜓 → 𝜒) → (𝜓 → (𝜒 ∧ 𝜑))))
3	2	a2i 15	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → (𝜒 ∧ 𝜑))))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  ssorduni  7784