Theorem anc2r 554

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		pm3.21 471	. . 3 ⊢ (𝜑 → (𝜒 → (𝜒 ∧ 𝜑)))
2	1	imim2d 57	. 2 ⊢ (𝜑 → ((𝜓 → 𝜒) → (𝜓 → (𝜒 ∧ 𝜑))))
3	2	a2i 14	1 ⊢ ((𝜑 → (𝜓 → 𝜒)) → (𝜑 → (𝜓 → (𝜒 ∧ 𝜑))))

Syntax hints:   → wi 4   ∧ wa 395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 396

This theorem is referenced by:  ssorduni  7606