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Theorem ins3keq 4219
 Description: Equality theorem for the Kuratowski insert three operator. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
ins3keq Ins3k Ins3k

Proof of Theorem ins3keq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eleq2 2414 . . . . . . 7
213anbi3d 1258 . . . . . 6
323exbidv 1629 . . . . 5
43anbi2d 684 . . . 4
542exbidv 1628 . . 3
65abbidv 2467 . 2
7 df-ins3k 4188 . 2 Ins3k
8 df-ins3k 4188 . 2 Ins3k
96, 7, 83eqtr4g 2410 1 Ins3k Ins3k
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358   w3a 934  wex 1541   wceq 1642   wcel 1710  cab 2339  csn 3737  copk 4057   Ins3k cins3k 4177 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-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-ins3k 4188 This theorem is referenced by:  ins3keqi  4221  ins3keqd  4223  ins3kexg  4306
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