Theorem anc2r 539

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		pm3.21 435	. . 3 ⊢ (φ → (χ → (χ ∧ φ)))
2	1	imim2d 48	. 2 ⊢ (φ → ((ψ → χ) → (ψ → (χ ∧ φ))))
3	2	a2i 12	1 ⊢ ((φ → (ψ → χ)) → (φ → (ψ → (χ ∧ φ))))

This proof depends on syntax axioms:   → wi 4   ∧ wa 358

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

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)