Theorem alimdv 1890

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 1537	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
2		alimdv.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
3	1, 2	alimdh 1478	1 ⊢ (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))

Syntax hints:   → wi 4  ∀wal 1362

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1458  ax-gen 1460  ax-17 1537

This theorem is referenced by:  2alimdv  1892  moim  2106  ralimdv2  2564  sstr2  3186  reuss2  3439  ssuni  3857  disjss2  4009  disjss1  4012  disjiun  4024  exmidsssnc  4232  soss  4345  alxfr  4492  ssrel  4747  ssrel2  4749  ssrelrel  4759  iotaval  5226  omnimkv  7215