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Theorem sbco3 2163
 Description: A composition law for substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbco3

Proof of Theorem sbco3
StepHypRef Expression
1 drsb1 2102 . . 3
2 sbequ12a 1946 . . . . 5
32alimi 1568 . . . 4
4 spsbbi 2151 . . . 4
53, 4syl 16 . . 3
61, 5bitr3d 247 . 2
7 sbco 2158 . . . 4
87sbbii 1665 . . 3
9 nfnae 2044 . . . 4
10 nfnae 2044 . . . 4
11 nfsb2 2092 . . . 4
129, 10, 11sbco2d 2162 . . 3
138, 12syl5rbbr 252 . 2
146, 13pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177  wal 1549  wsb 1658 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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