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Theorem cbvexdh 1798
Description: Deduction used to change bound variables, using implicit substitition, particularly useful in conjunction with dvelim 1890. (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 1416 . . 3
2 ax-17 1416 . . . 4
32hbex 1524 . . 3
4 cbvexdh.1 . . . . 5
5 cbvexdh.2 . . . . 5
6 cbvexdh.3 . . . . . 6
7 equcomi 1589 . . . . . . 7
8 bicom1 122 . . . . . . 7
97, 8imim12i 53 . . . . . 6
106, 9syl 14 . . . . 5
114, 5, 10equsexd 1614 . . . 4
12 simpr 103 . . . . 5
1312eximi 1488 . . . 4
1411, 13syl6bir 153 . . 3
151, 3, 14exlimdh 1484 . 2
161, 5eximdh 1499 . . . 4
17 19.12 1552 . . . 4
1816, 17syl6 29 . . 3
192a1i 9 . . . . 5
201, 19, 6equsexd 1614 . . . 4
21 simpr 103 . . . . 5
2221eximi 1488 . . . 4
2320, 22syl6bir 153 . . 3
244, 18, 23exlimd2 1483 . 2
2515, 24impbid 120 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   wceq 1242  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  cbvexd  1799
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