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Theorem ceqsrexv 2972

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	$/\$

(

)

**Proof of Theorem ceqsrexv**
Step	Hyp	Ref	Expression
1		df-rex 2620	. . 3 $/\$ $/\$ $/\$
2		an12 772	. . . 4 $/\$ $/\$ $/\$ $/\$
3	2	exbii 1582	. . 3 $/\$ $/\$ $/\$ $/\$
4	1, 3	bitr4i 243	. 2 $/\$ $/\$ $/\$
5		eleq1 2413	. . . . 5
6		ceqsrexv.1	. . . . 5
7	5, 6	anbi12d 691	. . . 4 $/\$ $/\$
8	7	ceqsexgv 2971	. . 3 $/\$ $/\$ $/\$
9	8	bianabs 850	. 2 $/\$ $/\$
10	4, 9	syl5bb 248	1 $/\$

Colors of variables: wff setvar class

Syntax hints:

wi 4

wb 176 $/\$ wa 358

wex 1541

wceq 1642

wcel 1710

wrex 2615

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334

This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 df-v 2861

This theorem is referenced by: ceqsrexbv 2973 ceqsrex2v 2974 fnasrn 5417 f1oiso 5499