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Theorem cnvss 4508
 Description: Subset theorem for converse. (Contributed by NM, 22-Mar-1998.)
Assertion
Ref Expression
cnvss

Proof of Theorem cnvss
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ssel 2939 . . . 4
2 df-br 3765 . . . 4
3 df-br 3765 . . . 4
41, 2, 33imtr4g 194 . . 3
54ssopab2dv 4015 . 2
6 df-cnv 4353 . 2
7 df-cnv 4353 . 2
85, 6, 73sstr4g 2986 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1393   wss 2917  cop 3378   class class class wbr 3764  copab 3817  ccnv 4344 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-in 2924  df-ss 2931  df-br 3765  df-opab 3819  df-cnv 4353 This theorem is referenced by:  cnveq  4509  rnss  4564  relcnvtr  4840  funss  4920  funcnvuni  4968  funres11  4971  funcnvres  4972  foimacnv  5144  tposss  5861
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