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Theorem sbco2 2158
Description: A composition law for substitution. (Contributed by NM, 30-Jun-1994.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 17-Sep-2018.)
Hypothesis
Ref Expression
sbco2.1
Assertion
Ref Expression
sbco2

Proof of Theorem sbco2
StepHypRef Expression
1 sbequ12 1992 . . . 4
2 sbequ 2117 . . . 4
31, 2bitr3d 255 . . 3
43sps 1865 . 2
5 nfnae 2058 . . 3
6 sbco2.1 . . . 4
76nfsb4 2131 . . 3
82a1i 11 . . 3
95, 7, 8sbied 2151 . 2
104, 9pm2.61i 164 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  A.wal 1393  F/wnf 1616  [wsb 1739
This theorem is referenced by:  sbco2d  2159  equsb3ALT  2177  elsb3  2178  elsb4  2179  sb7f  2197  sbco4lem  2209  sbco4  2210  2eu6OLD  2384  eqsb3  2577  clelsb3  2578  cbvab  2598  sbralie  3097  sbcco  3350  clelsb3f  27379  bj-clelsb3  34424  frege72  37963
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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