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Theorem gencbval 2596
Description: Change of bound variable using implicit substitution. (Contributed by NM, 17-May-1996.) (Proof rewritten by Jim Kingdon, 20-Jun-2018.)
Hypotheses
Ref Expression
gencbval.1  _V
gencbval.2
gencbval.3
gencbval.4
Assertion
Ref Expression
gencbval
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()   ()

Proof of Theorem gencbval
StepHypRef Expression
1 alcom 1364 . 2
2 gencbval.1 . . . 4  _V
3 gencbval.3 . . . . . . 7
4 gencbval.2 . . . . . . 7
53, 4imbi12d 223 . . . . . 6
65bicomd 129 . . . . 5
76eqcoms 2040 . . . 4
82, 7ceqsalv 2578 . . 3
98albii 1356 . 2
10 19.23v 1760 . . . 4
11 gencbval.4 . . . . . . 7
12 eqcom 2039 . . . . . . . . . 10
1312biimpi 113 . . . . . . . . 9
1413adantl 262 . . . . . . . 8
1514eximi 1488 . . . . . . 7
1611, 15sylbi 114 . . . . . 6
17 pm2.04 76 . . . . . 6
1816, 17mpdi 38 . . . . 5
19 ax-1 5 . . . . 5
2018, 19impbii 117 . . . 4
2110, 20bitri 173 . . 3
2221albii 1356 . 2
231, 9, 223bitr3i 199 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   wceq 1242  wex 1378   wcel 1390   _Vcvv 2551
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  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553
This theorem is referenced by: (None)
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