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Theorem cbval2 1976
 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 1874 . 2
3 cbval2.3 . . 3
43nfal 1874 . 2
5 nfv 1674 . . . . . 6
6 cbval2.2 . . . . . 6
75, 6nfim 1854 . . . . 5
8 nfv 1674 . . . . . 6
9 cbval2.4 . . . . . 6
108, 9nfim 1854 . . . . 5
11 cbval2.5 . . . . . . 7
1211expcom 435 . . . . . 6
1312pm5.74d 247 . . . . 5
147, 10, 13cbval 1970 . . . 4
15 19.21v 1910 . . . 4
16 19.21v 1910 . . . 4
1714, 15, 163bitr3i 275 . . 3
1817pm5.74ri 246 . 2
192, 4, 18cbval 1970 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369  wal 1368  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 1709  ax-7 1729  ax-10 1776  ax-11 1781  ax-12 1793  ax-13 1944 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591 This theorem is referenced by:  cbvex2  1977  cbval2v  1979  2moOLDOLD  2368  2eu6OLD  2378
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