Theorem difprsn2 4167

Description: Removal of a singleton from an unordered pair. (Contributed by Alexander van der Vekens, 5-Oct-2017.)

Assertion

Ref	Expression
difprsn2

Proof of Theorem difprsn2

Step	Hyp	Ref	Expression
1		prcom 4108	. . 3
2	1	difeq1i 3617	. 2
3		necom 2726	. . 3
4		difprsn1 4166	. . 3
5	3, 4	sylbi 195	. 2
6	2, 5	syl5eq 2510	1

Syntax hints:  ->wi 4  =wceq 1395  =/=wne 2652  \cdif 3472  {csn 4029  {cpr 4031

This theorem is referenced by:  f12dfv  6179  pmtrprfval  16512  cusgra2v  24462  frgra2v  24999  ldepsnlinc  33109

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-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030  df-pr 4032