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Theorem csbmpt12 4735
 Description: Move substitution into a maps-to notation. (Contributed by AV, 26-Sep-2019.)
Assertion
Ref Expression
csbmpt12
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   (,)

Proof of Theorem csbmpt12
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbopab 4733 . . 3
2 sbcan 3298 . . . . 5
3 sbcel12 3776 . . . . . . 7
4 csbconstg 3362 . . . . . . . 8
54eleq1d 2533 . . . . . . 7
63, 5syl5bb 265 . . . . . 6
7 sbceq2g 3783 . . . . . 6
86, 7anbi12d 725 . . . . 5
92, 8syl5bb 265 . . . 4
109opabbidv 4459 . . 3
111, 10syl5eq 2517 . 2
12 df-mpt 4456 . . 3
1312csbeq2i 3786 . 2
14 df-mpt 4456 . 2
1511, 13, 143eqtr4g 2530 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 376   wceq 1452   wcel 1904  wsbc 3255  csb 3349  copab 4453   cmpt 4454 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-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  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-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-opab 4455  df-mpt 4456 This theorem is referenced by:  csbmpt2  4736  esum2dlem  28987
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