Theorem alimdv 1927

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 1574	. 2 ⊢ (𝜑 → ∀𝑥𝜑)
2		alimdv.1	. 2 ⊢ (𝜑 → (𝜓 → 𝜒))
3	1, 2	alimdh 1515	1 ⊢ (𝜑 → (∀𝑥𝜓 → ∀𝑥𝜒))

Syntax hints:   → wi 4  ∀wal 1395

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1495  ax-gen 1497  ax-17 1574

This theorem is referenced by:  2alimdv  1929  moim  2144  ralimdv2  2602  sstr2  3234  reuss2  3487  ssuni  3915  disjss2  4067  disjss1  4070  disjiun  4083  exmidsssnc  4293  soss  4411  alxfr  4558  ssrel  4814  ssrel2  4816  ssrelrel  4826  iotaval  5298  omnimkv  7354