Theorem sseq2i 3035

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 3032	. 2 |- ( A = B -> ( C C_ A <-> C C_ B ) )
3	1, 2	ax-mp 7	1 |- ( C C_ A <-> C C_ B )

Syntax hints:   <-> wb 103   = wceq 1285   C_ wss 2984

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-in 2990  df-ss 2997

This theorem is referenced by:  sseqtri  3042  syl6sseq  3056  abss  3074  ssrab  3083  ssintrab  3685  iunpwss  3790  iotass  4951  dffun2  4979  ssimaex  5310  bj-ssom  11174