Theorem ceqsrexv 3233

Description: Elimination of a restricted existential quantifier, using implicit substitution. (Contributed by NM, 30-Apr-2004.)

Hypothesis

Ref	Expression
ceqsrexv.1

Assertion

Ref	Expression
ceqsrexv

Distinct variable groups:   ,   ,   ,

Proof of Theorem ceqsrexv

Step	Hyp	Ref	Expression
1		df-rex 2813	. . 3
2		an12 797	. . . 4
3	2	exbii 1667	. . 3
4	1, 3	bitr4i 252	. 2
5		eleq1 2529	. . . . 5
6		ceqsrexv.1	. . . . 5
7	5, 6	anbi12d 710	. . . 4
8	7	ceqsexgv 3232	. . 3
9	8	bianabs 880	. 2
10	4, 9	syl5bb 257	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  E.wrex 2808

This theorem is referenced by:  ceqsrexbv  3234  ceqsrex2v  3235  reuxfr2d  4675  f1oiso  6247  creur  10555  creui  10556  deg1ldg  22492  ulm2  22780  reuxfr3d  27388  rmxdiophlem  30957  expdiophlem1  30963  expdiophlem2  30964  eqlkr3  34826  diclspsn  36921

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-rex 2813  df-v 3111