Theorem eqsstr3i 3058

Description: Substitution of equality into a subclass relationship. (Contributed by NM, 19-Oct-1999.)

Hypotheses

Ref	Expression
eqsstr3.1	|- B = A
eqsstr3.2	|- B C_ C

Assertion

Ref	Expression
eqsstr3i	|- A C_ C

Proof of Theorem eqsstr3i

Step	Hyp	Ref	Expression
1		eqsstr3.1	. . 3 |- B = A
2	1	eqcomi 2093	. 2 |- A = B
3		eqsstr3.2	. 2 |- B C_ C
4	2, 3	eqsstri 3057	1 |- A C_ C

Syntax hints:   = wceq 1290   C_ wss 3000

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 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-11 1443  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071

This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-in 3006  df-ss 3013

This theorem is referenced by:  inss2  3222  dmv  4665  resasplitss  5203  ofrfval  5878  fnofval  5879  ofrval  5880  off  5882  ofres  5883  ofco  5887  dftpos4  6042  smores2  6073  caseinj  6834  djuinj  6841  bcm1k  10222  bcpasc  10228