Theorem eqsstrri 3212

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 3211	1 |- A C_ C

Syntax hints:   = wceq 1364   C_ wss 3153

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 3159  df-ss 3166

This theorem is referenced by:  inss2  3380  dmv  4878  resasplitss  5433  ofrfval  6139  ofvalg  6140  ofrval  6141  off  6143  ofres  6145  ofco  6149  dftpos4  6316  smores2  6347  caseinj  7148  djuinj  7165  bcm1k  10831  bcpasc  10837  nninfctlemfo  12177