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Theorem cbvex2 2083
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 14-Sep-2003.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 16-Jun-2019.)
Hypotheses
Ref Expression
cbval2.1
cbval2.2
cbval2.3
cbval2.4
cbval2.5
Assertion
Ref Expression
cbvex2
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)   (,,,)

Proof of Theorem cbvex2
StepHypRef Expression
1 cbval2.1 . . . . 5
21nfn 1957 . . . 4
3 cbval2.2 . . . . 5
43nfn 1957 . . . 4
5 cbval2.3 . . . . 5
65nfn 1957 . . . 4
7 cbval2.4 . . . . 5
87nfn 1957 . . . 4
9 cbval2.5 . . . . 5
109notbid 296 . . . 4
112, 4, 6, 8, 10cbval2 2082 . . 3
1211notbii 298 . 2
13 2exnaln 1698 . 2
14 2exnaln 1698 . 2
1512, 13, 143bitr4i 281 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wa 371  wal 1436  wex 1660  wnf 1664 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1661  df-nf 1665 This theorem is referenced by:  cbvex2v  2085  cbvopab  4490  cbvoprab12  6377
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