Theorem a17d 1617

Description: ax-17 1616 with antecedent. Useful in proofs of deduction versions of bound-variable hypothesis builders. (Contributed by NM, 1-Mar-2013.)

Assertion

Ref	Expression
a17d	⊢ (φ → (ψ → ∀xψ))

Distinct variable group:   ψ,x

Allowed substitution hint:   φ(x)

Proof of Theorem a17d

Step	Hyp	Ref	Expression
1		ax-17 1616	. 2 ⊢ (ψ → ∀xψ)
2	1	a1i 10	1 ⊢ (φ → (ψ → ∀xψ))

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-17 1616

This theorem is referenced by:  ax12w  1724  dvelimv  1939