Theorem anc2ri 557

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 22	. 2 ⊢ (𝜑 → 𝜑)
3	1, 2	jctird 527	1 ⊢ (𝜑 → (𝜓 → (𝜒 ∧ 𝜑)))

Syntax hints:   → wi 4   ∧ wa 396

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 397

This theorem is referenced by:  fv3  6792  bropopvvv  7930  bropfvvvvlem  7931  issiga  32080  ontopbas  34617  bj-gl4  34777  clsk1independent  41656