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Theorem csbcnvg 24037
 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 4261 . . . . 5
2 csbconstg 3265 . . . . . 6
3 csbconstg 3265 . . . . . 6
42, 3breq12d 4225 . . . . 5
51, 4bitrd 245 . . . 4
65opabbidv 4271 . . 3
7 csbopabg 4283 . . 3
8 df-cnv 4886 . . . 4
98a1i 11 . . 3
106, 7, 93eqtr4rd 2479 . 2
11 df-cnv 4886 . . 3
1211csbeq2i 3277 . 2
1310, 12syl6eqr 2486 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  wsbc 3161  csb 3251   class class class wbr 4212  copab 4265  ccnv 4877 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-cnv 4886
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