Theorem eqimssi 2107

Description: Infer subclass relationship from equality.

Hypothesis

Ref	Expression
eqimssi.1	|- A = B

Assertion

Ref	Expression
eqimssi	|- A (_ B

Proof of Theorem eqimssi

Step	Hyp	Ref	Expression
1		ssid 2076	. 2 |- A (_ A
2		eqimssi.1	. 2 |- A = B
3	1, 2	sseqtr 2089	1 |- A (_ B

Syntax hints:   = wceq 954   (_ wss 2043

This theorem is referenced by:  funi 3537  tz7.48-2 3948  trcl 4625  zorn2lem4 4771  om2uzf1o 6246  idcn 7716  cncfmet1 7858  1alg 10534  0alg 10569

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 960  ax-gen 961  ax-8 962  ax-10 964  ax-12 966  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-10o 1138  ax-16 1208  ax-11o 1216  ax-ext 1457

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-in 2047  df-ss 2049

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