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Theorem cocnvcnv2 5524
 Description: A composition is not affected by a double converse of its second argument. (Contributed by NM, 8-Oct-2007.)
Assertion
Ref Expression
cocnvcnv2

Proof of Theorem cocnvcnv2
StepHypRef Expression
1 cnvcnv2 5465 . . 3
21coeq2i 5168 . 2
3 resco 5516 . 2
4 relco 5510 . . 3
5 dfrel3 5469 . . 3
64, 5mpbi 208 . 2
72, 3, 63eqtr2i 2492 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395   cvv 3109  'ccnv 5003  |cres 5006  o.ccom 5008  Relwrel 5009 This theorem is referenced by:  dfdm2  5544  cofunex2g  6765  cnvtrrel  37782 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  df-co 5013  df-res 5016
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