Theorem imim12d 68

Description: Deduction combining antecedents and consequents. (Contributed by NM, 7-Aug-1994.) (Proof shortened by O'Cat, 30-Oct-2011.)

Hypotheses

Ref	Expression
imim12d.1	⊢ (φ → (ψ → χ))
imim12d.2	⊢ (φ → (θ → τ))

Assertion

Ref	Expression
imim12d	⊢ (φ → ((χ → θ) → (ψ → τ)))

Proof of Theorem imim12d

Step	Hyp	Ref	Expression
1		imim12d.1	. 2 ⊢ (φ → (ψ → χ))
2		imim12d.2	. . 3 ⊢ (φ → (θ → τ))
3	2	imim2d 48	. 2 ⊢ (φ → ((χ → θ) → (χ → τ)))
4	1, 3	syl5d 62	1 ⊢ (φ → ((χ → θ) → (ψ → τ)))

Syntax hints:   → wi 4

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

This theorem is referenced by:  imim1d  69  equveli  1988  mo  2226  rspcimdv  2957