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Theorem csbmpt12 4786
Description: Move substitution into a maps-to notation. (Contributed by AV, 26-Sep-2019.)
Assertion
Ref Expression
csbmpt12
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem csbmpt12
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbopab 4784 . . 3
2 sbcan 3370 . . . . 5
3 sbcel12 3823 . . . . . . 7
4 csbconstg 3447 . . . . . . . 8
54eleq1d 2526 . . . . . . 7
63, 5syl5bb 257 . . . . . 6
7 sbceq2g 3833 . . . . . 6
86, 7anbi12d 710 . . . . 5
92, 8syl5bb 257 . . . 4
109opabbidv 4515 . . 3
111, 10syl5eq 2510 . 2
12 df-mpt 4512 . . 3
1312csbeq2i 3836 . 2
14 df-mpt 4512 . 2
1511, 13, 143eqtr4g 2523 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  [.wsbc 3327  [_csb 3434  {copab 4509  e.cmpt 4510
This theorem is referenced by:  csbmpt2  4787
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-mpt 4512
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