Theorem spc2egv 3196

Description: Existential specialization with 2 quantifiers, using implicit substitution. (Contributed by NM, 3-Aug-1995.)

Hypothesis

Ref	Expression
spc2egv.1

Assertion

Ref	Expression
spc2egv

Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem spc2egv

Step	Hyp	Ref	Expression
1		elisset 3120	. . . 4
2		elisset 3120	. . . 4
3	1, 2	anim12i 566	. . 3
4		eeanv 1988	. . 3
5	3, 4	sylibr 212	. 2
6		spc2egv.1	. . . 4
7	6	biimprcd 225	. . 3
8	7	2eximdv 1712	. 2
9	5, 8	syl5com 30	1

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

This theorem is referenced by:  spc2gv  3197  spc2ev  3202  addsrpr  9473  mulsrpr  9474  0pthonv  24583  1pthon2v  24595  2pthon3v  24606  usg2wlk  24617  usg2wlkon  24618  dvnprodlem1  31743  tpres  32554

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-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-v 3111