Theorem 2alimi 1385

Description: Inference doubly quantifying both antecedent and consequent. (Contributed by NM, 3-Feb-2005.)

Hypothesis

Ref	Expression
alimi.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
2alimi	⊢ (∀𝑥∀𝑦𝜑 → ∀𝑥∀𝑦𝜓)

Proof of Theorem 2alimi

Step	Hyp	Ref	Expression
1		alimi.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	alimi 1384	. 2 ⊢ (∀𝑦𝜑 → ∀𝑦𝜓)
3	2	alimi 1384	1 ⊢ (∀𝑥∀𝑦𝜑 → ∀𝑥∀𝑦𝜓)

Syntax hints:   → wi 4  ∀wal 1282

This theorem was proved from axioms:  ax-mp 7  ax-5 1376  ax-gen 1378

This theorem is referenced by:  mo23  1982  mo3h  1994  spc2gv  2688  spc3gv  2690  euind  2779  reuind  2795  sbnfc2  2962  opelopabt  4017  ssrel  4446  ssrelrel  4458  fnoprabg  5622