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Theorem cbval2 2027
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 22-Dec-2003.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 22-Apr-2018.)
Hypotheses
Ref Expression
cbval2.1
cbval2.2
cbval2.3
cbval2.4
cbval2.5
Assertion
Ref Expression
cbval2
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem cbval2
StepHypRef Expression
1 cbval2.1 . . 3
21nfal 1947 . 2
3 cbval2.3 . . 3
43nfal 1947 . 2
5 nfv 1707 . . . . . 6
6 cbval2.2 . . . . . 6
75, 6nfim 1920 . . . . 5
8 nfv 1707 . . . . . 6
9 cbval2.4 . . . . . 6
108, 9nfim 1920 . . . . 5
11 cbval2.5 . . . . . . 7
1211expcom 435 . . . . . 6
1312pm5.74d 247 . . . . 5
147, 10, 13cbval 2021 . . . 4
15 19.21v 1729 . . . 4
16 19.21v 1729 . . . 4
1714, 15, 163bitr3i 275 . . 3
1817pm5.74ri 246 . 2
192, 4, 18cbval 2021 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  F/wnf 1616 This theorem is referenced by:  cbvex2  2028  cbval2v  2030  2eu6OLD  2384 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-13 1999 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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