Theorem imim3i 55

Description: Inference adding three nested antecedents. (Contributed by NM, 19-Dec-2006.)

Hypothesis

Ref	Expression
imim3i.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
imim3i	⊢ ((θ → φ) → ((θ → ψ) → (θ → χ)))

Proof of Theorem imim3i

Step	Hyp	Ref	Expression
1		imim3i.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	imim2i 13	. 2 ⊢ ((θ → φ) → (θ → (ψ → χ)))
3	2	a2d 23	1 ⊢ ((θ → φ) → ((θ → ψ) → (θ → χ)))

Syntax hints:   → wi 4

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

This theorem is referenced by:  pm2.83  71  pm5.74  235  bi3ant  280  pm3.43i  442  ax12olem3  1929  ceqsalt  2882