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Theorem cnvssrndm 5534
 Description: The converse is a subset of the cartesian product of range and domain. (Contributed by Mario Carneiro, 2-Jan-2017.)
Assertion
Ref Expression
cnvssrndm

Proof of Theorem cnvssrndm
StepHypRef Expression
1 relcnv 5379 . . 3
2 relssdmrn 5533 . . 3
31, 2ax-mp 5 . 2
4 df-rn 5015 . . 3
5 dfdm4 5200 . . 3
64, 5xpeq12i 5026 . 2
73, 6sseqtr4i 3536 1
 Colors of variables: wff setvar class Syntax hints:  C_wss 3475  X.cxp 5002  'ccnv 5003  domcdm 5004  rancrn 5005  Rel`wrel 5009 This theorem is referenced by:  wuncnv  9129  fcnvgreu  27514 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-dm 5014  df-rn 5015
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