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Theorem sbco3 2160
Description: A composition law for substitution. (Contributed by NM, 2-Jun-1993.) (Proof shortened by Wolf Lammen, 18-Sep-2018.)
Assertion
Ref Expression
sbco3

Proof of Theorem sbco3
StepHypRef Expression
1 drsb1 2118 . . 3
2 nfae 2056 . . . 4
3 sbequ12a 1994 . . . . 5
43sps 1865 . . . 4
52, 4sbbid 2144 . . 3
61, 5bitr3d 255 . 2
7 sbco 2154 . . . 4
87sbbii 1746 . . 3
9 nfnae 2058 . . . 4
10 nfnae 2058 . . . 4
11 nfsb2 2100 . . . 4
129, 10, 11sbco2d 2159 . . 3
138, 12syl5rbbr 260 . 2
146, 13pm2.61i 164 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184  A.wal 1393  [wsb 1739
This theorem is referenced by:  sbcom  2161
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
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