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Theorem cnvsn 5496
Description: Converse of a singleton of an ordered pair. (Contributed by NM, 11-May-1998.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypotheses
Ref Expression
cnvsn.1
cnvsn.2
Assertion
Ref Expression
cnvsn

Proof of Theorem cnvsn
StepHypRef Expression
1 cnvcnvsn 5490 . 2
2 cnvsn.2 . . . 4
3 cnvsn.1 . . . 4
42, 3relsnop 5112 . . 3
5 dfrel2 5462 . . 3
64, 5mpbi 208 . 2
71, 6eqtr3i 2488 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  e.wcel 1818   cvv 3109  {csn 4029  <.cop 4035  `'ccnv 5003  Relwrel 5009
This theorem is referenced by:  op2ndb  5497  cnvsng  5499  f1osn  5858  1sdom  7742  ex-cnv  25158
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-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  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  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-cnv 5012
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