Theorem ss2in 2236

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 2234	. 2 |- (A (_ B -> (A i^i C) (_ (B i^i C))
2		sslin 2235	. 2 |- (C (_ D -> (B i^i C) (_ (B i^i D))
3	1, 2	sylan9ss 2075	1 |- ((A (_ B /\ C (_ D) -> (A i^i C) (_ (B i^i D))

Syntax hints:   -> wi 3   /\ wa 223   i^i cin 2046   (_ wss 2047

This theorem is referenced by:  undom 4438  tgclt 7624  innei 7736  opnin 7869  5oa 9606  mdsl0 10237  fgsb 10570  fgsbOLD 10571  fgsb2 10580

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-v 1812  df-in 2051  df-ss 2053

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