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Theorem elsb4 2179
 Description: Substitution applied to an atomic membership wff. (Contributed by Rodolfo Medina, 3-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
elsb4
Distinct variable group:   ,

Proof of Theorem elsb4
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1707 . . 3
21sbco2 2158 . 2
3 nfv 1707 . . . 4
4 elequ2 1823 . . . 4
53, 4sbie 2149 . . 3
65sbbii 1746 . 2
7 nfv 1707 . . 3
8 elequ2 1823 . . 3
97, 8sbie 2149 . 2
102, 6, 93bitr3i 275 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  [wsb 1739 This theorem is referenced by:  nfnid  4681 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-9 1822  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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