Theorem rexrab2 3267

Description: Existential quantification over a class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.)

Hypothesis

Ref	Expression
ralab2.1

Assertion

Ref	Expression
rexrab2

Distinct variable groups:   ,   ,   ,   ,   ,

Proof of Theorem rexrab2

Step	Hyp	Ref	Expression
1		df-rab 2816	. . 3
2	1	rexeqi 3059	. 2
3		ralab2.1	. . 3
4	3	rexab2 3266	. 2
5		anass 649	. . . 4
6	5	exbii 1667	. . 3
7		df-rex 2813	. . 3
8	6, 7	bitr4i 252	. 2
9	2, 4, 8	3bitri 271	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  E.wex 1612  e.wcel 1818  {cab 2442  E.wrex 2808  {crab 2811

This theorem is referenced by:  frminex  4864  sstotbnd3  30272

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-11 1842  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-nfc 2607  df-rex 2813  df-rab 2816