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Theorem csbmpt2 4756
 Description: Move substitution into the second part of a maps-to notation. (Contributed by AV, 26-Sep-2019.)
Assertion
Ref Expression
csbmpt2
Distinct variable groups:   ,   ,   ,,
Allowed substitution hints:   ()   ()   (,)

Proof of Theorem csbmpt2
StepHypRef Expression
1 csbmpt12 4755 . 2
2 csbconstg 3414 . . 3
32mpteq1d 4507 . 2
41, 3eqtrd 2470 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1437   wcel 1870  csb 3401   cmpt 4484 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407  ax-sep 4548  ax-nul 4556  ax-pr 4661 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-fal 1443  df-ex 1660  df-nf 1664  df-sb 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ne 2627  df-ral 2787  df-v 3089  df-sbc 3306  df-csb 3402  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-opab 4485  df-mpt 4486 This theorem is referenced by:  matgsum  19393
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