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Theorem cbvex2 1988
 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 1840 . . . 4
3 cbval2.2 . . . . 5
43nfn 1840 . . . 4
5 cbval2.3 . . . . 5
65nfn 1840 . . . 4
7 cbval2.4 . . . . 5
87nfn 1840 . . . 4
9 cbval2.5 . . . . 5
109notbid 294 . . . 4
112, 4, 6, 8, 10cbval2 1987 . . 3
1211notbii 296 . 2
13 2exnaln 1621 . 2
14 2exnaln 1621 . 2
1512, 13, 143bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wa 369  wal 1368  wex 1587  wnf 1590 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591 This theorem is referenced by:  cbvex2v  1991  2eu6OLD  2381  cbvopab  4471  cbvoprab12  6272
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