Theorem sseq12i 2087

Description: An equality inference for the subclass relationship. (The proof was shortened by Eric Schmidt, 26-Jan-2007.)

Hypotheses

Ref	Expression
sseq1i.1	|- A = B
sseq12i.2	|- C = D

Assertion

Ref	Expression
sseq12i	|- (A (_ C <-> B (_ D)

Proof of Theorem sseq12i

Step	Hyp	Ref	Expression
1		sseq1i.1	. 2 |- A = B
2		sseq12i.2	. 2 |- C = D
3		sseq12 2084	. 2 |- ((A = B /\ C = D) -> (A (_ C <-> B (_ D))
4	1, 2, 3	mp2an 697	1 |- (A (_ C <-> B (_ D)

Syntax hints:   <-> wb 146   = wceq 956   (_ wss 2047

This theorem is referenced by:  3sstr3 2099  3sstr4 2100  3sstr3g 2101  3sstr4g 2102  ss2rab 2123  rabss2 2129  ssopab2 2822  shlub 9346  pjord 10101  mdsldmd1 10258

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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