Theorem sseq2i 3206

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 3203	. 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 1364   C_ wss 3153

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-in 3159  df-ss 3166

This theorem is referenced by:  sseqtri  3213  sseqtrdi  3227  abss  3248  ssrab  3257  ssintrab  3893  iunpwss  4004  iotass  5232  dffun2  5264  ssimaex  5618  pw1fin  6966  pw1dc0el  6967  ss1o0el1o  6969  isstructim  12632  isstructr  12633  issubm  13044  grpissubg  13264  issubrng  13695  bj-ssom  15428  ss1oel2o  15484