Theorem anc2ri 541

Description: Deduction conjoining antecedent to right of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 7-Dec-2012.)

Hypothesis

Ref	Expression
anc2ri.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
anc2ri	⊢ (φ → (ψ → (χ ∧ φ)))

Proof of Theorem anc2ri

Step	Hyp	Ref	Expression
1		anc2ri.1	. 2 ⊢ (φ → (ψ → χ))
2		id 19	. 2 ⊢ (φ → φ)
3	1, 2	jctird 528	1 ⊢ (φ → (ψ → (χ ∧ φ)))

Syntax hints:   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by:  equvini  1987  fv3  5342