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Theorem sbex 2128
 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 2062 . . 3
2 sbal 2127 . . . 4
3 sbn 2062 . . . . 5
43albii 1566 . . . 4
52, 4bitri 240 . . 3
61, 5xchbinx 301 . 2
7 df-ex 1542 . . 3
87sbbii 1653 . 2
9 df-ex 1542 . 2
106, 8, 93bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 176  wal 1540  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:  sbmo  2234  sbabel  2515  sbcex2  3095  sbcexg  3096
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