Theorem otelxp1 4027

Description: The first member of an ordered triple of classes in a cross product belongs to first cross product argument.

Assertion

Ref	Expression
otelxp1	|- (<.<.A, B>., C>. e. ((R X. S) X. T) -> A e. R)

Proof of Theorem otelxp1

Step	Hyp	Ref	Expression
1		opelxp1 4026	. 2 |- (<.<.A, B>., C>. e. ((R X. S) X. T) -> <.A, B>. e. (R X. S))
2		opelxp1 4026	. 2 |- (<.A, B>. e. (R X. S) -> A e. R)
3	1, 2	syl 12	1 |- (<.<.A, B>., C>. e. ((R X. S) X. T) -> A e. R)

Syntax hints:   -> wi 3   e. wcel 1300  <.cop 3046   X. cxp 3984

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 1304  ax-gen 1305  ax-8 1306  ax-9 1307  ax-10 1308  ax-11 1309  ax-12 1310  ax-14 1312  ax-17 1317  ax-4 1319  ax-5o 1321  ax-6o 1324  ax-9o 1481  ax-10o 1500  ax-16 1580  ax-11o 1588  ax-ext 1865  ax-sep 3438  ax-nul 3445  ax-pow 3481  ax-pr 3524

This theorem depends on definitions:  df-bi 164  df-or 241  df-an 242  df-ex 1327  df-sb 1536  df-clab 1872  df-cleq 1877  df-clel 1880  df-ne 2019  df-v 2294  df-dif 2597  df-un 2600  df-in 2603  df-ss 2605  df-nul 2876  df-pw 3035  df-sn 3049  df-pr 3050  df-op 3053  df-opab 3396  df-xp 4000

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