Theorem imim1d 69

Description: Deduction adding nested consequents. (Contributed by NM, 3-Apr-1994.) (Proof shortened by Wolf Lammen, 12-Sep-2012.)

Hypothesis

Ref	Expression
imim1d.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
imim1d	⊢ (φ → ((χ → θ) → (ψ → θ)))

Proof of Theorem imim1d

Step	Hyp	Ref	Expression
1		imim1d.1	. 2 ⊢ (φ → (ψ → χ))
2		idd 21	. 2 ⊢ (φ → (θ → θ))
3	1, 2	imim12d 68	1 ⊢ (φ → ((χ → θ) → (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:  imim1  70  expt  148  imbi1d  308  meredith  1404  19.23tOLD  1819  ax12olem3  1929  morimv  2252  2mo  2282  sstr2  3280  ssralv  3331  preaddccan2  4456  spacind  6288  nchoicelem12  6301