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Theorem csbcnvg 4723
 Description: Move class substitution in and out of the converse of a function. (Contributed by Thierry Arnoux, 8-Feb-2017.)
Assertion
Ref Expression
csbcnvg

Proof of Theorem csbcnvg
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 sbcbrg 3982 . . . . 5
2 csbconstg 3016 . . . . . 6
3 csbconstg 3016 . . . . . 6
42, 3breq12d 3942 . . . . 5
51, 4bitrd 187 . . . 4
65opabbidv 3994 . . 3
7 csbopabg 4006 . . 3
8 df-cnv 4547 . . . 4
98a1i 9 . . 3
106, 7, 93eqtr4rd 2183 . 2
11 df-cnv 4547 . . 3
1211csbeq2i 3029 . 2
1310, 12syl6eqr 2190 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331   wcel 1480  wsbc 2909  csb 3003   class class class wbr 3929  copab 3988  ccnv 4538 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-sbc 2910  df-csb 3004  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930  df-opab 3990  df-cnv 4547 This theorem is referenced by: (None)
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