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Theorem sbel2x 2202
 Description: Elimination of double substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbel2x
Distinct variable groups:   ,,   ,   ,,
Allowed substitution hints:   (,)

Proof of Theorem sbel2x
StepHypRef Expression
1 sbelx 2201 . . . . 5
21anbi2i 676 . . . 4
32exbii 1592 . . 3
4 sbelx 2201 . . 3
5 exdistr 1929 . . 3
63, 4, 53bitr4i 269 . 2
7 anass 631 . . 3
872exbii 1593 . 2
96, 8bitr4i 244 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1550  wsb 1658 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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