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Theorem cbvexdh 1898
 Description: Deduction used to change bound variables, using implicit substitition, particularly useful in conjunction with dvelim 1992. (Contributed by NM, 2-Jan-2002.) (Proof rewritten by Jim Kingdon, 30-Dec-2017.)
Hypotheses
Ref Expression
cbvexdh.1
cbvexdh.2
cbvexdh.3
Assertion
Ref Expression
cbvexdh
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)   ()

Proof of Theorem cbvexdh
StepHypRef Expression
1 ax-17 1506 . . 3
2 ax-17 1506 . . . 4
32hbex 1615 . . 3
4 cbvexdh.1 . . . . 5
5 cbvexdh.2 . . . . 5
6 cbvexdh.3 . . . . . 6
7 equcomi 1680 . . . . . . 7
8 bicom1 130 . . . . . . 7
97, 8imim12i 59 . . . . . 6
106, 9syl 14 . . . . 5
114, 5, 10equsexd 1707 . . . 4
12 simpr 109 . . . . 5
1312eximi 1579 . . . 4
1411, 13syl6bir 163 . . 3
151, 3, 14exlimdh 1575 . 2
161, 5eximdh 1590 . . . 4
17 19.12 1643 . . . 4
1816, 17syl6 33 . . 3
192a1i 9 . . . . 5
201, 19, 6equsexd 1707 . . . 4
21 simpr 109 . . . . 5
2221eximi 1579 . . . 4
2320, 22syl6bir 163 . . 3
244, 18, 23exlimd2 1574 . 2
2515, 24impbid 128 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1329   wceq 1331  wex 1468 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  cbvexd  1899
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