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Theorem sbco2 2161
 Description: A composition law for substitution. (Contributed by NM, 30-Jun-1994.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypothesis
Ref Expression
sbco2.1
Assertion
Ref Expression
sbco2

Proof of Theorem sbco2
StepHypRef Expression
1 sbco2.1 . . . . . 6
21sbid2 2159 . . . . 5
3 sbequ 2138 . . . . 5
42, 3syl5bbr 251 . . . 4
5 sbequ12 1944 . . . 4
64, 5bitr3d 247 . . 3
76sps 1770 . 2
8 nfnae 2044 . . . 4
91nfs1 2096 . . . . 5
109nfsb4 2156 . . . 4
114a1i 11 . . . 4
128, 10, 11sbied 2123 . . 3
1312bicomd 193 . 2
147, 13pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177  wal 1549  wnf 1553  wsb 1658 This theorem is referenced by:  sbco2d  2162  equsb3  2177  elsb3  2178  elsb4  2179  sb7f  2195  2eu6  2365  eqsb3  2536  clelsb3  2537  sbralie  2937  sbcco  3175  clelsb3f  23963 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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