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Theorem csbcnvg 23234
 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 4151 . . . . 5
2 csbconstg 3171 . . . . . 6
3 csbconstg 3171 . . . . . 6
42, 3breq12d 4115 . . . . 5
51, 4bitrd 244 . . . 4
65opabbidv 4161 . . 3
7 csbopabg 4173 . . 3
8 df-cnv 4776 . . . 4
98a1i 10 . . 3
106, 7, 93eqtr4rd 2401 . 2
11 df-cnv 4776 . . . 4
1211csbeq2i 3183 . . 3
1312a1i 10 . 2
1410, 13eqtr4d 2393 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1642   wcel 1710  wsbc 3067  csb 3157   class class class wbr 4102  copab 4155  ccnv 4767 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-rab 2628  df-v 2866  df-sbc 3068  df-csb 3158  df-dif 3231  df-un 3233  df-in 3235  df-ss 3242  df-nul 3532  df-if 3642  df-sn 3722  df-pr 3723  df-op 3725  df-br 4103  df-opab 4157  df-cnv 4776
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