MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  csbmpt2 Unicode version

Theorem csbmpt2 4787
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:   ,   ,   , ,

Proof of Theorem csbmpt2
StepHypRef Expression
1 csbmpt12 4786 . 2
2 csbconstg 3447 . . 3
32mpteq1d 4533 . 2
41, 3eqtrd 2498 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  [_csb 3434  e.cmpt 4510
This theorem is referenced by:  matgsum  18939
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-ral 2812  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
  Copyright terms: Public domain W3C validator