Theorem sseq2i 3296

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 3293	. 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 176   = wceq 1642   C_ wss 3257

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259

This theorem is referenced by:  sseqtri  3303  syl6sseq  3317  abss  3335  ssrab  3344  ssindif0  3604  difcom  3634  ssunsn2  3865  ssunpr  3868  sspr  3869  sstp  3870  ssintrab  3949  iunpwss  4055  pwadjoin  4119  pw1fnf1o  5855