Theorem alimdv 1621

Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 3-Apr-1994.)

Hypothesis

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

Assertion

Ref	Expression
alimdv	⊢ (φ → (∀xψ → ∀xχ))

Distinct variable group:   φ,x

Allowed substitution hints:   ψ(x)   χ(x)

Proof of Theorem alimdv

Step	Hyp	Ref	Expression
1		ax-17 1616	. 2 ⊢ (φ → ∀xφ)
2		alimdv.1	. 2 ⊢ (φ → (ψ → χ))
3	1, 2	alimdh 1563	1 ⊢ (φ → (∀xψ → ∀xχ))

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1546  ax-5 1557  ax-17 1616

This theorem is referenced by:  2alimdv  1623  ax16i  2046  ax16ALT2  2048  morimv  2252  ralimdv2  2695  mo2icl  3016  sstr2  3280  reuss2  3536  ssuni  3914  iotaval  4351  spfinsfincl  4540  eqfnfv  5393  dff3  5421  clos1conn  5880