Theorem sseq2i 3228

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 3225	. 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 1373   C_ wss 3174

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-in 3180  df-ss 3187

This theorem is referenced by:  sseqtri  3235  sseqtrdi  3249  abss  3270  ssrab  3279  ssintrab  3922  iunpwss  4033  iotass  5268  dffun2  5300  ssimaex  5663  pw1fin  7033  pw1dc0el  7034  ss1o0el1o  7036  isstructim  12961  isstructr  12962  issubm  13419  grpissubg  13645  issubrng  14076  umgredg  15849  bj-ssom  16071  ss1oel2o  16127