Theorem sseq12 2084

Description: Equality theorem for the subclass relationship.

Assertion

Ref	Expression
sseq12	|- ((A = B /\ C = D) -> (A (_ C <-> B (_ D))

Proof of Theorem sseq12

Step	Hyp	Ref	Expression
1		sseq1 2082	. 2 |- (A = B -> (A (_ C <-> B (_ C))
2		sseq2 2083	. 2 |- (C = D -> (B (_ C <-> B (_ D))
3	1, 2	sylan9bb 540	1 |- ((A = B /\ C = D) -> (A (_ C <-> B (_ D))

Syntax hints:   -> wi 3   <-> wb 146   /\ wa 223   = wceq 956   (_ wss 2047

This theorem is referenced by:  sseq12i 2087  funcnvuni 3564

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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