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Theorem sbco3 1848
 Description: A composition law for substitution. (Contributed by NM, 5-Aug-1993.) (Proof rewritten by Jim Kingdon, 22-Mar-2018.)
Assertion
Ref Expression
sbco3

Proof of Theorem sbco3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 sbco3xzyz 1847 . . 3
21sbbii 1648 . 2
3 ax-17 1419 . . 3
43sbco2h 1838 . 2
5 ax-17 1419 . . 3
65sbco2h 1838 . 2
72, 4, 63bitr3i 199 1
 Colors of variables: wff set class Syntax hints:   wb 98  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:  sbcom  1849
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