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Theorem sbex 2258
 Description: Move existential quantifier in and out of substitution. (Contributed by NM, 27-Sep-2003.)
Assertion
Ref Expression
sbex
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)

Proof of Theorem sbex
StepHypRef Expression
1 sbn 2185 . . 3
2 sbal 2257 . . . 4
3 sbn 2185 . . . . 5
43albii 1687 . . . 4
52, 4bitri 252 . . 3
61, 5xchbinx 311 . 2
7 df-ex 1660 . . 3
87sbbii 1793 . 2
9 df-ex 1660 . 2
106, 8, 93bitr4i 280 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 187  wal 1435  wex 1659  wsb 1786 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-ex 1660  df-nf 1664  df-sb 1787 This theorem is referenced by:  sbmo  2311  sbabel  2616  sbabelOLD  2617  sbcex2  3350  sbcexgOLD  36762
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