Theorem xpss2 4392

Description: Subset relation for cross product. (Contributed by Jeff Hankins, 30-Aug-2009.)

Assertion

Ref	Expression
xpss2	|- (A C_ B -> ( C X. A) C_ ( C X. B))

Proof of Theorem xpss2

Step	Hyp	Ref	Expression
1		ssid 2958	. 2 |- C C_ C
2		xpss12 4388	. 2 |- (( C C_ C /\ A C_ B) -> ( C X. A) C_ ( C X. B))
3	1, 2	mpan 400	1 |- (A C_ B -> ( C X. A) C_ ( C X. B))

Syntax hints:   -> wi 4   C_ wss 2911   X. cxp 4286

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019

This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-in 2918  df-ss 2925  df-opab 3810  df-xp 4294

This theorem is referenced by:  ssxp2  4701  xpdom3m  6244  axresscn  6746