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Theorem iineq1 3983
Description: Equality theorem for restricted existential quantifier. (Contributed by NM, 27-Jun-1998.)
Assertion
Ref Expression
iineq1
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem iineq1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 raleq 2807 . . 3
21abbidv 2467 . 2
3 df-iin 3972 . 2
4 df-iin 3972 . 2
52, 3, 43eqtr4g 2410 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wceq 1642   wcel 1710  cab 2339  wral 2614  ciin 3970
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  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-iin 3972
This theorem is referenced by:  iinrab2  4029  riin0  4039
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