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Theorem vtocl2gaf 2588
Description: Implicit substitution of 2 classes for 2 setvar variables. (Contributed by NM, 10-Aug-2013.)
Hypotheses
Ref Expression
vtocl2gaf.a  F/_
vtocl2gaf.b  F/_
vtocl2gaf.c  F/_
vtocl2gaf.1  F/
vtocl2gaf.2  F/
vtocl2gaf.3
vtocl2gaf.4
vtocl2gaf.5  C  D
Assertion
Ref Expression
vtocl2gaf  C  D
Distinct variable groups:   ,, C   , D,
Allowed substitution hints:   (,)   (,)   (,)   (,)   (,)

Proof of Theorem vtocl2gaf
StepHypRef Expression
1 vtocl2gaf.a . . 3  F/_
2 vtocl2gaf.b . . 3  F/_
3 vtocl2gaf.c . . 3  F/_
41nfel1 2161 . . . . 5  F/  C
5 nfv 1394 . . . . 5  F/  D
64, 5nfan 1430 . . . 4  F/  C  D
7 vtocl2gaf.1 . . . 4  F/
86, 7nfim 1437 . . 3  F/  C  D
92nfel1 2161 . . . . 5  F/  C
103nfel1 2161 . . . . 5  F/  D
119, 10nfan 1430 . . . 4  F/  C  D
12 vtocl2gaf.2 . . . 4  F/
1311, 12nfim 1437 . . 3  F/  C  D
14 eleq1 2073 . . . . 5  C  C
1514anbi1d 438 . . . 4  C  D  C  D
16 vtocl2gaf.3 . . . 4
1715, 16imbi12d 223 . . 3  C  D  C  D
18 eleq1 2073 . . . . 5  D  D
1918anbi2d 437 . . . 4  C  D  C  D
20 vtocl2gaf.4 . . . 4
2119, 20imbi12d 223 . . 3  C  D  C  D
22 vtocl2gaf.5 . . 3  C  D
231, 2, 3, 8, 13, 17, 21, 22vtocl2gf 2583 . 2  C  D  C  D
2423pm2.43i 43 1  C  D
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1223   F/wnf 1322   wcel 1366   F/_wnfc 2138
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-io 614  ax-5 1309  ax-7 1310  ax-gen 1311  ax-ie1 1355  ax-ie2 1356  ax-8 1368  ax-10 1369  ax-11 1370  ax-i12 1371  ax-bnd 1372  ax-4 1373  ax-17 1392  ax-i9 1396  ax-ial 1400  ax-i5r 1401  ax-ext 1995
This theorem depends on definitions:  df-bi 110  df-tru 1226  df-nf 1323  df-sb 1619  df-clab 2000  df-cleq 2006  df-clel 2009  df-nfc 2140  df-v 2528
This theorem is referenced by:  vtocl2ga  2589  ovmpt2s  5535  ov2gf  5536  ovi3  5548
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