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Theorem cbvex2 1991
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 14-Sep-2003.) (Revised by Mario Carneiro, 6-Oct-2016.)
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 . . 3
21nfex 1865 . 2
3 cbval2.3 . . 3
43nfex 1865 . 2
5 nfv 1629 . . . . . 6
6 cbval2.2 . . . . . 6
75, 6nfan 1846 . . . . 5
8 nfv 1629 . . . . . 6
9 cbval2.4 . . . . . 6
108, 9nfan 1846 . . . . 5
11 cbval2.5 . . . . . . 7
1211expcom 425 . . . . . 6
1312pm5.32d 621 . . . . 5
147, 10, 13cbvex 1983 . . . 4
15 19.42v 1928 . . . 4
16 19.42v 1928 . . . 4
1714, 15, 163bitr3i 267 . . 3
18 pm5.32 618 . . 3
1917, 18mpbir 201 . 2
202, 4, 19cbvex 1983 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550  wnf 1553 This theorem is referenced by:  cbvex2v  1993  2eu6  2365  cbvopab  4268  cbvoprab12  6138 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554
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