Theorem 2alimi 1560

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 1559	. 2 ⊢ (∀yφ → ∀yψ)
3	2	alimi 1559	1 ⊢ (∀x∀yφ → ∀x∀yψ)

Syntax hints:   → wi 4  ∀wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-gen 1546  ax-5 1557

This theorem is referenced by:  mo  2226  2mo  2282  2eu6  2289  euind  3024  reuind  3040  sbnfc2  3197  spfininduct  4541  opelopabt  4700  fvopab4t  5386  fnoprabg  5586