Theorem qdass 4129

Description: Two ways to write an unordered quadruple. (Contributed by Mario Carneiro, 5-Jan-2016.)

Assertion

Ref	Expression
qdass

Proof of Theorem qdass

Step	Hyp	Ref	Expression
1		unass 3660	. 2
2		df-tp 4034	. . 3
3	2	uneq1i 3653	. 2
4		df-pr 4032	. . 3
5	4	uneq2i 3654	. 2
6	1, 3, 5	3eqtr4ri 2497	1

Syntax hints:  =wceq 1395  u.cun 3473  {csn 4029  {cpr 4031  {ctp 4033

This theorem is referenced by:  ex-pw  25150

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-v 3111  df-un 3480  df-pr 4032  df-tp 4034