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Theorem csbmpt22g 31802
 Description: Move class substitution in and out of maps-to notation for operations. (Contributed by ML, 25-Oct-2020.)
Assertion
Ref Expression
csbmpt22g
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   ()   (,,)   ()   (,,)   (,,)

Proof of Theorem csbmpt22g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csboprabg 31801 . . 3
2 sbcan 3298 . . . . 5
3 sbcan 3298 . . . . . . 7
4 sbcel12 3776 . . . . . . . . 9
5 csbconstg 3362 . . . . . . . . . 10
65eleq1d 2533 . . . . . . . . 9
74, 6syl5bb 265 . . . . . . . 8
8 sbcel12 3776 . . . . . . . . 9
9 csbconstg 3362 . . . . . . . . . 10
109eleq1d 2533 . . . . . . . . 9
118, 10syl5bb 265 . . . . . . . 8
127, 11anbi12d 725 . . . . . . 7
133, 12syl5bb 265 . . . . . 6
14 sbceq2g 3783 . . . . . 6
1513, 14anbi12d 725 . . . . 5
162, 15syl5bb 265 . . . 4
1716oprabbidv 6364 . . 3
181, 17eqtrd 2505 . 2
19 df-mpt2 6313 . . 3
2019csbeq2i 3786 . 2
21 df-mpt2 6313 . 2
2218, 20, 213eqtr4g 2530 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 376   wceq 1452   wcel 1904  wsbc 3255  csb 3349  coprab 6309   cmpt2 6310 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-fal 1458  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rab 2765  df-v 3033  df-sbc 3256  df-csb 3350  df-dif 3393  df-in 3397  df-ss 3404  df-nul 3723  df-oprab 6312  df-mpt2 6313 This theorem is referenced by:  csbfinxpg  31850
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