Theorem nelprd 4051

Description: If an element doesn't match the items in an unordered pair, it is not in the unordered pair, deduction version. (Contributed by Alexander van der Vekens, 25-Jan-2018.)

Hypotheses

Ref	Expression
nelprd.1
nelprd.2

Assertion

Ref	Expression
nelprd

Proof of Theorem nelprd

Step	Hyp	Ref	Expression
1		nelprd.1	. 2
2		nelprd.2	. 2
3		neanior 2782	. . 3
4		elpri 4049	. . . 4
5	4	con3i 135	. . 3
6	3, 5	sylbi 195	. 2
7	1, 2, 6	syl2anc 661	1

Syntax hints:  -.wn 3  ->wi 4  \/wo 368  /\wa 369  =wceq 1395  e.wcel 1818  =/=wne 2652  {cpr 4031

This theorem is referenced by:  renfdisj  9668  pmtrprfv3  16479  perfectlem2  23505  usgra2pthlem1  32353

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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  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-un 3480  df-sn 4030  df-pr 4032