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Theorem r3al 2360
Description: Triple restricted universal quantification. (Contributed by NM, 19-Nov-1995.)
Assertion
Ref Expression
r3al  C  C
Distinct variable groups:   ,,   ,,   ,
Allowed substitution hints:   (,,)   ()   (,)    C(,,)

Proof of Theorem r3al
StepHypRef Expression
1 df-ral 2305 . 2  C  C
2 r2al 2337 . . 3  C  C
32ralbii 2324 . 2  C  C
4 3anass 888 . . . . . . . . 9  C  C
54imbi1i 227 . . . . . . . 8  C  C
6 impexp 250 . . . . . . . 8  C  C
75, 6bitri 173 . . . . . . 7  C  C
87albii 1356 . . . . . 6  C  C
9 19.21v 1750 . . . . . 6  C  C
108, 9bitri 173 . . . . 5  C  C
1110albii 1356 . . . 4  C  C
12 19.21v 1750 . . . 4  C  C
1311, 12bitri 173 . . 3  C  C
1413albii 1356 . 2  C  C
151, 3, 143bitr4i 201 1  C  C
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   w3a 884  wal 1240   wcel 1390  wral 2300
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305
This theorem is referenced by:  pocl  4031  soss  4042
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