Theorem sseq2i 3275

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 3272	. 2 |- ( A = B -> ( C C_ A <-> C C_ B ) )
3	1, 2	ax-mp 5	1 |- ( C C_ A <-> C C_ B )

This proof depends on syntax axioms:   <-> wb 105   = wceq 1402   C_ wss 3220

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-in 3226  df-ss 3233

This theorem is used by:  sseqtri  3282  sseqtrdi  3296  abss  3317  ssrab  3326  ssintrab  3993  iunpwss  4104  iotass  5358  dffun2  5390  ssimaex  5767  pw1fin  7221  pw1dc0el  7222  ss1o0el1o  7224  isstructim  13424  isstructr  13425  issubm  13838  grpissubg  14056  issubrng  14616  umgredg  16591  bj-ssom  17167  ss1oel2o  17222  exmidnotnotr  17241