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Theorem otelxp1 4874
Description: The first member of an ordered triple of classes in a Cartesian product belongs to first Cartesian product argument. (Contributed by NM, 28-May-2008.)
Assertion
Ref Expression
otelxp1  |-  ( <. <. A ,  B >. ,  C >.  e.  (
( R  X.  S
)  X.  T )  ->  A  e.  R
)

Proof of Theorem otelxp1
StepHypRef Expression
1 opelxp1 4872 . 2  |-  ( <. <. A ,  B >. ,  C >.  e.  (
( R  X.  S
)  X.  T )  ->  <. A ,  B >.  e.  ( R  X.  S ) )
2 opelxp1 4872 . 2  |-  ( <. A ,  B >.  e.  ( R  X.  S
)  ->  A  e.  R )
31, 2syl 17 1  |-  ( <. <. A ,  B >. ,  C >.  e.  (
( R  X.  S
)  X.  T )  ->  A  e.  R
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    e. wcel 1904   <.cop 3965    X. cxp 4837
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639
This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-opab 4455  df-xp 4845
This theorem is referenced by: (None)
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