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Theorem cbvexd 1983
 Description: Deduction used to change bound variables, using implicit substitution, particularly useful in conjunction with dvelim 2036. (Contributed by NM, 2-Jan-2002.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypotheses
Ref Expression
cbvald.1
cbvald.2
cbvald.3
Assertion
Ref Expression
cbvexd
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)   ()

Proof of Theorem cbvexd
StepHypRef Expression
1 cbvald.1 . . . 4
2 cbvald.2 . . . . 5
32nfnd 1838 . . . 4
4 cbvald.3 . . . . 5
5 notbi 295 . . . . 5
64, 5syl6ib 226 . . . 4
71, 3, 6cbvald 1982 . . 3
87notbid 294 . 2
9 df-ex 1588 . 2
10 df-ex 1588 . 2
118, 9, 103bitr4g 288 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184  wal 1368  wex 1587  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 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591 This theorem is referenced by:  cbvexdva  1990  vtoclgft  3118  dfid3  4737  axrepndlem2  8860  axunnd  8863  axpowndlem2  8865  axpowndlem2OLD  8866  axpownd  8870  axregndlem2  8872  axinfndlem1  8875  axacndlem4  8880  wl-mo2dnae  28535  wl-mo2t  28536
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