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Theorem cbvex2 2005
 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 1843 . 2
3 cbval2.3 . . 3
43nfex 1843 . 2
5 nfv 1619 . . . . . 6
6 cbval2.2 . . . . . 6
75, 6nfan 1824 . . . . 5
8 nfv 1619 . . . . . 6
9 cbval2.4 . . . . . 6
108, 9nfan 1824 . . . . 5
11 cbval2.5 . . . . . . 7
1211expcom 424 . . . . . 6
1312pm5.32d 620 . . . . 5
147, 10, 13cbvex 1985 . . . 4
15 19.42v 1905 . . . 4
16 19.42v 1905 . . . 4
1714, 15, 163bitr3i 266 . . 3
18 pm5.32 617 . . 3
1917, 18mpbir 200 . 2
202, 4, 19cbvex 1985 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wex 1541  wnf 1544 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  cbvex2v  2007  2eu6  2289  cbvopab  4630  cbvoprab12  5569
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