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Theorem elsb4 2104
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 1619 . . 3  F/
21sbco2 2086 . 2
3 nfv 1619 . . . 4  F/
4 elequ2 1715 . . . 4
53, 4sbie 2038 . . 3
65sbbii 1653 . 2
7 nfv 1619 . . 3  F/
8 elequ2 1715 . . 3
97, 8sbie 2038 . 2
102, 6, 93bitr3i 266 1
Colors of variables: wff setvar class
Syntax hints:   wb 176  wsb 1648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649
This theorem is referenced by: (None)
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