Theorem ins3keqi 4222

Description: Equality inference for Kuratowski insert three operator. (Contributed by SF, 12-Jan-2015.)

Hypothesis

Ref	Expression
inskeqi.1	⊢ A = B

Assertion

Ref	Expression
ins3keqi	⊢ Ins3k A = Ins3k B

Proof of Theorem ins3keqi

Step	Hyp	Ref	Expression
1		inskeqi.1	. 2 ⊢ A = B
2		ins3keq 4220	. 2 ⊢ (A = B → Ins3k A = Ins3k B)
3	1, 2	ax-mp 5	1 ⊢ Ins3k A = Ins3k B

Syntax hints:   = wceq 1642   Ins3_k cins3k 4178

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 4189

This theorem is referenced by: (None)