Theorem a1dd 42

Description: Deduction introducing a nested embedded antecedent. (Contributed by NM, 17-Dec-2004.) (Proof shortened by O'Cat, 15-Jan-2008.)

Hypothesis

Ref	Expression
a1dd.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
a1dd	⊢ (φ → (ψ → (θ → χ)))

Proof of Theorem a1dd

Step	Hyp	Ref	Expression
1		a1dd.1	. 2 ⊢ (φ → (ψ → χ))
2		ax-1 6	. 2 ⊢ (χ → (θ → χ))
3	1, 2	syl6 29	1 ⊢ (φ → (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:  merco2  1501  ax12b  1689  nfsb4t  2080  lenltfin  4469  tfinltfinlem1  4500  xpexr  5109  eqfnfv  5392  dff3  5420  spacind  6287