Theorem opi1 4719

Description: One of the two elements in an ordered pair. (Contributed by NM, 15-Jul-1993.) (Revised by Mario Carneiro, 26-Apr-2015.) (Avoid depending on this detail.)

Hypotheses

Ref	Expression
opi1.1
opi1.2

Assertion

Ref	Expression
opi1

Proof of Theorem opi1

Step	Hyp	Ref	Expression
1		snex 4693	. . 3
2	1	prid1 4138	. 2
3		opi1.1	. . 3
4		opi1.2	. . 3
5	3, 4	dfop 4216	. 2
6	2, 5	eleqtrri 2544	1

Syntax hints:  e.wcel 1818  cvv 3109  {csn 4029  {cpr 4031  <.cop 4035

This theorem is referenced by:  opth1  4725  opth  4726

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036