Theorem imim2d 48

Description: Deduction adding nested antecedents. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
imim2d.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
imim2d	⊢ (φ → ((θ → ψ) → (θ → χ)))

Proof of Theorem imim2d

Step	Hyp	Ref	Expression
1		imim2d.1	. . 3 ⊢ (φ → (ψ → χ))
2	1	a1d 22	. 2 ⊢ (φ → (θ → (ψ → χ)))
3	2	a2d 23	1 ⊢ (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:  imim2  49  embantd  50  imim12d  68  anc2r  539  pm5.31  571  dedlem0b  919  nic-ax  1438  nic-axALT  1439  19.23t  1800  nfimd  1808  spimt  1974  ssuni  3914  weds  5939  spacind  6288