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Theorem cbvexdOLD7 29672
 Description: Deduction used to change bound variables, using implicit substitution, particularly useful in conjunction with dvelimOLD7 29676. (Contributed by NM, 2-Jan-2002.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypotheses
Ref Expression
cbvald.1OLD7
cbvald.2OLD7
cbvald.3OLD7
Assertion
Ref Expression
cbvexdOLD7
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)   ()

Proof of Theorem cbvexdOLD7
StepHypRef Expression
1 cbvald.1OLD7 . . . 4
2 cbvald.2OLD7 . . . . 5
32nfnd 1809 . . . 4
4 cbvald.3OLD7 . . . . 5
5 notbi 287 . . . . 5
64, 5syl6ib 218 . . . 4
71, 3, 6cbvaldOLD7 29671 . . 3
87notbid 286 . 2
9 df-ex 1551 . 2
10 df-ex 1551 . 2
118, 9, 103bitr4g 280 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177  wal 1549  wex 1550  wnf 1553 This theorem is referenced by:  cbvexdvaOLD7  29674 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-11 1761  ax-12 1950  ax-7v 29379  ax-7OLD7 29615 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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