Theorem pm2.43d 44

Description: Deduction absorbing redundant antecedent. (Contributed by NM, 18-Aug-1993.) (Proof shortened by O'Cat, 28-Nov-2008.)

Hypothesis

Ref	Expression
pm2.43d.1	⊢ (φ → (ψ → (ψ → χ)))

Assertion

Ref	Expression
pm2.43d	⊢ (φ → (ψ → χ))

Proof of Theorem pm2.43d

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (ψ → ψ)
2		pm2.43d.1	. 2 ⊢ (φ → (ψ → (ψ → χ)))
3	1, 2	mpdi 38	1 ⊢ (φ → (ψ → 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:  loolinALT  95  ax12  1935  ax10lem4  1941  ax12from12o  2156  rgen2a  2681  rspct  2949  ncfinraise  4482  funssres  5145  2elresin  5195