Theorem eximdv 1801

Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 27-Apr-1994.)

Hypothesis

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

Assertion

Ref	Expression
eximdv	|- ( ph -> ( E. x ps -> E. x ch ) )

Distinct variable group:   ph, x

Allowed substitution hints:   ps( x)   ch( x)

Proof of Theorem eximdv

Step	Hyp	Ref	Expression
1		ax-17 1459	. 2 |- ( ph -> A. x ph )
2		alimdv.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	eximdh 1542	1 |- ( ph -> ( E. x ps -> E. x ch ) )

Syntax hints:   -> wi 4   E.wex 1421

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-17 1459  ax-ial 1467

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  2eximdv  1803  reximdv2  2460  cgsexg  2634  spc3egv  2689  euind  2779  ssel  2993  reupick  3248  reximdva0m  3263  uniss  3622  eusvnfb  4204  coss1  4509  coss2  4510  dmss  4552  dmcosseq  4621  funssres  4962  imain  5001  brprcneu  5191  fv3  5218  dffo4  5336  dffo5  5337  f1eqcocnv  5451  dmaddpq  6569  dmmulpq  6570  recexprlemlol  6816  recexprlemupu  6818  ioom  9269