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Theorem csbcnvgALT 5010
 Description: Move class substitution in and out of the converse of a function. Version of csbcnv 5009 with a sethood antecedent but depending on fewer axioms. (Contributed by Thierry Arnoux, 8-Feb-2017.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
csbcnvgALT

Proof of Theorem csbcnvgALT
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 sbcbr123 4448 . . . . 5
2 csbconstg 3388 . . . . . 6
3 csbconstg 3388 . . . . . 6
42, 3breq12d 4410 . . . . 5
51, 4syl5bb 259 . . . 4
65opabbidv 4460 . . 3
7 csbopabgALT 4725 . . 3
8 df-cnv 4833 . . . 4
98a1i 11 . . 3
106, 7, 93eqtr4rd 2456 . 2
11 df-cnv 4833 . . 3
1211csbeq2i 3789 . 2
1310, 12syl6eqr 2463 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1407   wcel 1844  wsbc 3279  csb 3375   class class class wbr 4397  copab 4454  ccnv 4824 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382 This theorem depends on definitions:  df-bi 187  df-or 370  df-an 371  df-3an 978  df-tru 1410  df-fal 1413  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-rab 2765  df-v 3063  df-sbc 3280  df-csb 3376  df-dif 3419  df-un 3421  df-in 3423  df-ss 3430  df-nul 3741  df-if 3888  df-sn 3975  df-pr 3977  df-op 3981  df-br 4398  df-opab 4456  df-cnv 4833 This theorem is referenced by: (None)
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