Theorem a2d 23

Description: Deduction distributing an embedded antecedent. (Contributed by NM, 23-Jun-1994.)

Hypothesis

Ref	Expression
a2d.1	⊢ (φ → (ψ → (χ → θ)))

Assertion

Ref	Expression
a2d	⊢ (φ → ((ψ → χ) → (ψ → θ)))

Proof of Theorem a2d

Step	Hyp	Ref	Expression
1		a2d.1	. 2 ⊢ (φ → (ψ → (χ → θ)))
2		ax-2 7	. 2 ⊢ ((ψ → (χ → θ)) → ((ψ → χ) → (ψ → θ)))
3	1, 2	syl 15	1 ⊢ (φ → ((ψ → χ) → (ψ → θ)))

Syntax hints:   → wi 4

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

This theorem is referenced by:  mpdd  36  imim2d  48  imim3i  55  loowoz  96  ralimdaa  2692  reuss2  3536  ltfintri  4467  spfinsfincl  4540  spfininduct  4541  funfvima2  5461  clos1conn  5880  leconnnc  6219  nchoicelem17  6306