Theorem 2alimi 1432

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 1431	. 2 ⊢ (∀𝑦𝜑 → ∀𝑦𝜓)
3	2	alimi 1431	1 ⊢ (∀𝑥∀𝑦𝜑 → ∀𝑥∀𝑦𝜓)

Syntax hints:   → wi 4  ∀wal 1329

This theorem was proved from axioms:  ax-mp 5  ax-5 1423  ax-gen 1425

This theorem is referenced by:  mo23  2040  mo3h  2052  spc2gv  2776  spc3gv  2778  euind  2871  reuind  2889  sbnfc2  3060  opelopabt  4184  ssrel  4627  ssrelrel  4639  fnoprabg  5872