Theorem exlimdvv 1637

Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 31-Jul-1995.)

Hypothesis

Ref	Expression
exlimdvv.1	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
exlimdvv	|- (ph -> (E.xE.yps -> ch))

Distinct variable groups:   ch,x   ph,x   ch,y   ph,y

Allowed substitution hints:   ps(x,y)

Proof of Theorem exlimdvv

Step	Hyp	Ref	Expression
1		exlimdvv.1	. . 3 |- (ph -> (ps -> ch))
2	1	exlimdv 1636	. 2 |- (ph -> (E.yps -> ch))
3	2	exlimdv 1636	1 |- (ph -> (E.xE.yps -> ch))

Syntax hints:   -> wi 4  E.wex 1541

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616

This theorem depends on definitions:  df-bi 177  df-ex 1542

This theorem is referenced by:  ncfinlower  4484  sfin112  4530  sfindbl  4531  sfinltfin  4536  funsi  5521  fntxp  5805  fnpprod  5844  fundmen  6044  ce0addcnnul  6180  ce0nnulb  6183  ceclb  6184  fce  6189  fnfrec  6321