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Theorem ins3keqd 4223
 Description: Equality deduction for Kuratowski insert three operator. (Contributed by SF, 12-Jan-2015.)
Hypothesis
Ref Expression
inskeqd.1 (φA = B)
Assertion
Ref Expression
ins3keqd (φIns3k A = Ins3k B)

Proof of Theorem ins3keqd
StepHypRef Expression
1 inskeqd.1 . 2 (φA = B)
2 ins3keq 4219 . 2 (A = BIns3k A = Ins3k B)
31, 2syl 15 1 (φIns3k A = Ins3k B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   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:  cokeq2  4231  imagekeq  4244
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