Theorem 2alimi 1480

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 1479	. 2 ⊢ (∀𝑦𝜑 → ∀𝑦𝜓)
3	2	alimi 1479	1 ⊢ (∀𝑥∀𝑦𝜑 → ∀𝑥∀𝑦𝜓)

Syntax hints:   → wi 4  ∀wal 1371

This theorem was proved from axioms:  ax-mp 5  ax-5 1471  ax-gen 1473

This theorem is referenced by:  mo23  2096  mo3h  2108  spc2gv  2868  spc3gv  2870  euind  2964  reuind  2982  sbnfc2  3158  opelopabt  4315  ssrel  4770  ssrelrel  4782  fundif  5326  fnoprabg  6058