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Theorem elixp2b 25257
 Description: The base class of the elements of a nuple. (Contributed by FL, 6-Jun-2011.) (Revised by Mario Carneiro, 12-Aug-2016.)
Assertion
Ref Expression
elixp2b
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem elixp2b
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-ixp 6834 . . . 4
2 simpr 447 . . . . 5
32ss2abi 3258 . . . 4
41, 3eqsstri 3221 . . 3
54sseli 3189 . 2
6 fveq1 5540 . . . . 5
76eleq1d 2362 . . . 4
87ralbidv 2576 . . 3
98elabg 2928 . 2
105, 9mpbid 201 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 358   wceq 1632   wcel 1696  cab 2282  wral 2556   wfn 5266  cfv 5271  cixp 6833 This theorem is referenced by:  bclelnu  25258  dstr  25274 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-v 2803  df-in 3172  df-ss 3179  df-uni 3844  df-br 4040  df-iota 5235  df-fv 5279  df-ixp 6834
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