Theorem spc2ev 3202

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

Hypotheses

Ref	Expression
spc2ev.1
spc2ev.2
spc2ev.3

Assertion

Ref	Expression
spc2ev

Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem spc2ev

Step	Hyp	Ref	Expression
1		spc2ev.1	. 2
2		spc2ev.2	. 2
3		spc2ev.3	. . 3
4	3	spc2egv 3196	. 2
5	1, 2, 4	mp2an 672	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  cvv 3109

This theorem is referenced by:  relop  5158  endisj  7624  dcomex  8848  axcnre  9562  constr3cyclpe  24663  3v3e3cycl2  24664  qqhval2  27963  itg2addnclem3  30068  wlkc  32350

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