Theorem gencbval 3155

Description: Change of bound variable using implicit substitution. (Contributed by NM, 17-May-1996.)

Hypotheses

Ref	Expression
gencbval.1
gencbval.2
gencbval.3
gencbval.4

Assertion

Ref	Expression
gencbval

Distinct variable groups:   ,   ,   ,   ,   ,

Proof of Theorem gencbval

Step	Hyp	Ref	Expression
1		gencbval.1	. . . 4
2		gencbval.2	. . . . 5
3	2	notbid 294	. . . 4
4		gencbval.3	. . . 4
5		gencbval.4	. . . 4
6	1, 3, 4, 5	gencbvex 3153	. . 3
7		exanali 1670	. . 3
8		exanali 1670	. . 3
9	6, 7, 8	3bitr3i 275	. 2
10	9	con4bii 297	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818  cvv 3109

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