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Theorem sbex 2207
Description: Move existential quantifier in and out of substitution. (Contributed by NM, 27-Sep-2003.)
Assertion
Ref Expression
sbex
Distinct variable groups:   ,   ,

Proof of Theorem sbex
StepHypRef Expression
1 sbn 2132 . . 3
2 sbal 2206 . . . 4
3 sbn 2132 . . . . 5
43albii 1640 . . . 4
52, 4bitri 249 . . 3
61, 5xchbinx 310 . 2
7 df-ex 1613 . . 3
87sbbii 1746 . 2
9 df-ex 1613 . 2
106, 8, 93bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184  A.wal 1393  E.wex 1612  [wsb 1739
This theorem is referenced by:  sbmo  2335  sbabel  2650  sbabelOLD  2651  sbcex2  3381  sbcexgOLD  3382
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-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
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