Theorem sseq2i 3255

Description: An equality inference for the subclass relationship. (Contributed by NM, 30-Aug-1993.)

Hypothesis

Ref	Expression
sseq1i.1	|- A = B

Assertion

Ref	Expression
sseq2i	|- ( C C_ A <-> C C_ B )

Proof of Theorem sseq2i

Step	Hyp	Ref	Expression
1		sseq1i.1	. 2 |- A = B
2		sseq2 3252	. 2 |- ( A = B -> ( C C_ A <-> C C_ B ) )
3	1, 2	ax-mp 5	1 |- ( C C_ A <-> C C_ B )

Syntax hints:   <-> wb 105   = wceq 1398   C_ wss 3201

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-in 3207  df-ss 3214

This theorem is referenced by:  sseqtri  3262  sseqtrdi  3276  abss  3297  ssrab  3306  ssintrab  3956  iunpwss  4067  iotass  5311  dffun2  5343  ssimaex  5716  pw1fin  7145  pw1dc0el  7146  ss1o0el1o  7148  isstructim  13176  isstructr  13177  issubm  13635  grpissubg  13861  issubrng  14294  umgredg  16086  bj-ssom  16652  ss1oel2o  16707  exmidnotnotr  16727