Theorem eqsstr3 2092

Description: Substitution of equality into a subclass relationship.

Hypotheses

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

Assertion

Ref	Expression
eqsstr3	|- A (_ C

Proof of Theorem eqsstr3

Step	Hyp	Ref	Expression
1		eqsstr3.1	. . 3 |- B = A
2	1	eqcomi 1479	. 2 |- A = B
3		eqsstr3.2	. 2 |- B (_ C
4	2, 3	eqsstr 2091	1 |- A (_ C

Syntax hints:   = wceq 956   (_ wss 2047

This theorem is referenced by:  inss2 2231  dmv 3327  cfom 4916  dfnn2 5936  infmap2 7581  lmfval 7925  pjoml4 9530  5oa 9606  3oa 9613  bdopssadj 10014

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 962  ax-gen 963  ax-8 964  ax-10 966  ax-12 968  ax-17 971  ax-4 973  ax-5o 975  ax-6o 978  ax-9o 1123  ax-10o 1140  ax-16 1210  ax-11o 1218  ax-ext 1459

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 981  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-in 2051  df-ss 2053

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