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Theorem cbval2 1989
 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:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)   (,,,)

Proof of Theorem cbval2
StepHypRef Expression
1 cbval2.1 . . 3
21nfal 1864 . 2
3 cbval2.3 . . 3
43nfal 1864 . 2
5 nfv 1629 . . . . . 6
6 cbval2.2 . . . . . 6
75, 6nfim 1832 . . . . 5
8 nfv 1629 . . . . . 6
9 cbval2.4 . . . . . 6
108, 9nfim 1832 . . . . 5
11 cbval2.5 . . . . . . 7
1211expcom 425 . . . . . 6
1312pm5.74d 239 . . . . 5
147, 10, 13cbval 1982 . . . 4
15 19.21v 1913 . . . 4
16 19.21v 1913 . . . 4
1714, 15, 163bitr3i 267 . . 3
1817pm5.74ri 238 . 2
192, 4, 18cbval 1982 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wnf 1553 This theorem is referenced by:  cbval2v  1992  2mo  2358  2eu6  2365 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-ex 1551  df-nf 1554
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