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Theorem sbex 2204
 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 2117 . . 3
2 sbal 2203 . . . 4
3 sbn 2117 . . . . 5
43albii 1575 . . . 4
52, 4bitri 241 . . 3
61, 5xchbinx 302 . 2
7 df-ex 1551 . . 3
87sbbii 1665 . 2
9 df-ex 1551 . 2
106, 8, 93bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177  wal 1549  wex 1550  wsb 1658 This theorem is referenced by:  sbmo  2310  sbabel  2597  sbcex2  3202  sbcexg  3203 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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