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Theorem xpss1 4391
 Description: Subset relation for cross product. (Contributed by Jeff Hankins, 30-Aug-2009.)
Assertion
Ref Expression
xpss1 (AB → (A × 𝐶) ⊆ (B × 𝐶))

Proof of Theorem xpss1
StepHypRef Expression
1 ssid 2958 . 2 𝐶𝐶
2 xpss12 4388 . 2 ((AB 𝐶𝐶) → (A × 𝐶) ⊆ (B × 𝐶))
31, 2mpan2 401 1 (AB → (A × 𝐶) ⊆ (B × 𝐶))
 Colors of variables: wff set class Syntax hints:   → wi 4   ⊆ wss 2911   × 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:  ssres2  4581  ssxp1  4700  funssxp  5003  tposssxp  5805  tpostpos2  5821  tfrlemibfn  5883  enq0enq  6414
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