Theorem difpr 4169

Description: Removing two elements as pair of elements corresponds to removing each of the two elements as singletons. (Contributed by Alexander van der Vekens, 13-Jul-2018.)

Assertion

Ref	Expression
difpr

Proof of Theorem difpr

Step	Hyp	Ref	Expression
1		df-pr 4032	. . 3
2	1	difeq2i 3618	. 2
3		difun1 3757	. 2
4	2, 3	eqtri 2486	1

Syntax hints:  =wceq 1395  \cdif 3472  u.cun 3473  {csn 4029  {cpr 4031

This theorem is referenced by:  nbgrassvwo2  24438

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-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-pr 4032