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Theorem cbvexd 2009
 Description: Deduction used to change bound variables, using implicit substitution, particularly useful in conjunction with dvelim 2016. (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 1791 . . . 4
4 cbvald.3 . . . . 5
5 notbi 286 . . . . 5
64, 5syl6ib 217 . . . 4
71, 3, 6cbvald 2008 . . 3
87notbid 285 . 2
9 df-ex 1542 . 2
10 df-ex 1542 . 2
118, 9, 103bitr4g 279 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176  wal 1540  wex 1541  wnf 1544 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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:  cbvexdva  2011  vtoclgft  2905  dfid3  4768
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