Theorem sseq2i 3090

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 3087	. 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 104   = wceq 1314   C_ wss 3037

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097

This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-in 3043  df-ss 3050

This theorem is referenced by:  sseqtri  3097  syl6sseq  3111  abss  3132  ssrab  3141  ssintrab  3760  iunpwss  3870  iotass  5063  dffun2  5091  ssimaex  5436  isstructim  11816  isstructr  11817  bj-ssom  12826  ss1oel2o  12881