Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  iineq1 Structured version   Unicode version

Theorem iineq1 4099
 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 2896 . . 3
21abbidv 2549 . 2
3 df-iin 4088 . 2
4 df-iin 4088 . 2
52, 3, 43eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cab 2421  wral 2697  ciin 4086 This theorem is referenced by:  iinrab2  4146  riin0  4156  iin0  4365  xpriindi  5003  cmpfi  17463  ptbasfi  17605  fclsval  18032  taylfval  20267  polvalN  30639 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  ax-ext 2416 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  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-iin 4088
 Copyright terms: Public domain W3C validator