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Theorem sbco2d 1840
 Description: A composition law for substitution. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
sbco2d.1
sbco2d.2
sbco2d.3
Assertion
Ref Expression
sbco2d

Proof of Theorem sbco2d
StepHypRef Expression
1 sbco2d.2 . . . . 5
2 sbco2d.3 . . . . 5
31, 2hbim1 1462 . . . 4
43sbco2h 1838 . . 3
5 sbco2d.1 . . . . . 6
65sbrim 1830 . . . . 5
76sbbii 1648 . . . 4
81sbrim 1830 . . . 4
97, 8bitri 173 . . 3
105sbrim 1830 . . 3
114, 9, 103bitr3i 199 . 2
1211pm5.74ri 170 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241  wsb 1645 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646 This theorem is referenced by: (None)
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