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Theorem cbvexh 1685
 Description: Rule used to change bound variables, using implicit substitition. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Feb-2015.)
Hypotheses
Ref Expression
cbvexh.1
cbvexh.2
cbvexh.3
Assertion
Ref Expression
cbvexh

Proof of Theorem cbvexh
StepHypRef Expression
1 cbvexh.2 . . . 4
21hbex 1572 . . 3
3 cbvexh.1 . . . . 5
4 cbvexh.3 . . . . . . 7
54bicomd 139 . . . . . 6
65equcoms 1641 . . . . 5
73, 6equsex 1663 . . . 4
8 simpr 108 . . . . 5
98eximi 1536 . . . 4
107, 9sylbir 133 . . 3
112, 10exlimih 1529 . 2
123hbex 1572 . . 3
131, 4equsex 1663 . . . 4
14 simpr 108 . . . . 5
1514eximi 1536 . . . 4
1613, 15sylbir 133 . . 3
1712, 16exlimih 1529 . 2
1811, 17impbii 124 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1287   wceq 1289  wex 1426 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472 This theorem depends on definitions:  df-bi 115 This theorem is referenced by:  cbvex  1686  sb8eh  1783  cbvexv  1843  euf  1953  mopick  2026
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