Theorem eqsstrri 3213

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
eqsstrri	|- A C_ C

Proof of Theorem eqsstrri

Step	Hyp	Ref	Expression
1		eqsstr3.1	. . 3 |- B = A
2	1	eqcomi 2197	. 2 |- A = B
3		eqsstr3.2	. 2 |- B C_ C
4	2, 3	eqsstri 3212	1 |- A C_ C

Syntax hints:   = wceq 1364   C_ wss 3154

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-in 3160  df-ss 3167

This theorem is referenced by:  inss2  3381  dmv  4879  resasplitss  5434  ofrfval  6141  ofvalg  6142  ofrval  6143  off  6145  ofres  6147  ofco  6151  dftpos4  6318  smores2  6349  caseinj  7150  djuinj  7167  bcm1k  10834  bcpasc  10840  nninfctlemfo  12180