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Theorem sbco3 2137
 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 2091 . . 3
2 nfa1 1845 . . . 4
3 sbequ12a 1963 . . . . 5
43sps 1814 . . . 4
52, 4sbbid 2118 . . 3
61, 5bitr3d 255 . 2
7 sbco 2129 . . . 4
87sbbii 1718 . . 3
9 nfnae 2031 . . . 4
10 nfna1 1851 . . . 4
11 nfsb2 2073 . . . 4
129, 10, 11sbco2d 2136 . . 3
138, 12syl5rbbr 260 . 2
146, 13pm2.61i 164 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 184  wal 1377  wsb 1711 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1597  df-nf 1600  df-sb 1712 This theorem is referenced by:  sbcom  2139
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