Theorem ss2in 2226

Description: Intersection of subclasses.

Assertion

Ref	Expression
ss2in	|- ((A (_ B /\ C (_ D) -> (A i^i C) (_ (B i^i D))

Proof of Theorem ss2in

Step	Hyp	Ref	Expression
1		ssrin 2224	. 2 |- (A (_ B -> (A i^i C) (_ (B i^i C))
2		sslin 2225	. 2 |- (C (_ D -> (B i^i C) (_ (B i^i D))
3	1, 2	sylan9ss 2065	1 |- ((A (_ B /\ C (_ D) -> (A i^i C) (_ (B i^i D))

Syntax hints:   -> wi 3   /\ wa 223   i^i cin 2036   (_ wss 2037

This theorem is referenced by:  undom 4418  tgclt 7566  innei 7677  opnin 7809  5oa 9523  mdsl0 10145  fgsb 10444  fgsb2 10449

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-12 965  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 978  df-sb 1168  df-clab 1457  df-cleq 1462  df-clel 1465  df-v 1803  df-in 2041  df-ss 2043

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