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Theorem rexpssxrxp 7924
Description: The Cartesian product of standard reals are a subset of the Cartesian product of extended reals (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
rexpssxrxp (ℝ × ℝ) ⊆ (ℝ* × ℝ*)

Proof of Theorem rexpssxrxp
StepHypRef Expression
1 ressxr 7923 . 2 ℝ ⊆ ℝ*
2 xpss12 4695 . 2 ((ℝ ⊆ ℝ* ∧ ℝ ⊆ ℝ*) → (ℝ × ℝ) ⊆ (ℝ* × ℝ*))
31, 1, 2mp2an 423 1 (ℝ × ℝ) ⊆ (ℝ* × ℝ*)
Colors of variables: wff set class
Syntax hints:  wss 3102   × cxp 4586  cr 7733  *cxr 7913
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-in 3108  df-ss 3115  df-opab 4028  df-xp 4594  df-xr 7918
This theorem is referenced by:  ltrelxr  7940
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