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Theorem sbel2x 2203
Description: Elimination of double substitution. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 29-Sep-2018.)
Assertion
Ref Expression
sbel2x
Distinct variable group:   , ,

Proof of Theorem sbel2x
StepHypRef Expression
1 nfv 1707 . . 3
2 nfv 1707 . . 3
31, 22sb5rf 2195 . 2
4 ancom 450 . . . 4
54anbi1i 695 . . 3
652exbii 1668 . 2
7 excom 1849 . 2
83, 6, 73bitri 271 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  E.wex 1612  [wsb 1739
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-an 371  df-ex 1613  df-nf 1617  df-sb 1740
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