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Theorem sbel2x 2125
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 2124 . . . . 5
21anbi2i 675 . . . 4
32exbii 1582 . . 3
4 sbelx 2124 . . 3
5 exdistr 1906 . . 3
63, 4, 53bitr4i 268 . 2
7 anass 630 . . 3
872exbii 1583 . 2
96, 8bitr4i 243 1
Colors of variables: wff setvar class
Syntax hints:   wb 176   wa 358  wex 1541  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-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  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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