Theorem 2alimi 1560

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

Hypothesis

Ref	Expression
alimi.1	|- (ph -> ps)

Assertion

Ref	Expression
2alimi	|- (A.xA.yph -> A.xA.yps)

Proof of Theorem 2alimi

Step	Hyp	Ref	Expression
1		alimi.1	. . 3 |- (ph -> ps)
2	1	alimi 1559	. 2 |- (A.yph -> A.yps)
3	2	alimi 1559	1 |- (A.xA.yph -> A.xA.yps)

Syntax hints:   -> wi 4  A.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  3023  reuind  3039  sbnfc2  3196  spfininduct  4540  opelopabt  4699  fvopab4t  5385  fnoprabg  5585