Theorem ssres 3385

Description: Subclass theorem for restriction.

Assertion

Ref	Expression
ssres	|- (A (_ B -> (A |` C) (_ (B |` C))

Proof of Theorem ssres

Step	Hyp	Ref	Expression
1		ssrin 2234	. 2 |- (A (_ B -> (A i^i (C X. V)) (_ (B i^i (C X. V)))
2		df-res 3190	. 2 |- (A |` C) = (A i^i (C X. V))
3		df-res 3190	. 2 |- (B |` C) = (B i^i (C X. V))
4	1, 2, 3	3sstr4g 2102	1 |- (A (_ B -> (A |` C) (_ (B |` C))

Syntax hints:   -> wi 3  Vcvv 1811   i^i cin 2046   (_ wss 2047   X. cxp 3168   |` cres 3172

This theorem is referenced by:  imass1 3432  sspg 8387  ssps 8389  sspn 8395

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  df-res 3190

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