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Theorem csbidmg 2896
Description: Idempotent law for class substitutions. (Contributed by NM, 1-Mar-2008.)
Assertion
Ref Expression
csbidmg (A 𝑉A / xA / xB = A / xB)
Distinct variable group:   x,A
Allowed substitution hints:   B(x)   𝑉(x)

Proof of Theorem csbidmg
StepHypRef Expression
1 elex 2560 . 2 (A 𝑉A V)
2 csbnest1g 2895 . . 3 (A V → A / xA / xB = A / xA / xB)
3 csbconstg 2858 . . . 4 (A V → A / xA = A)
43csbeq1d 2852 . . 3 (A V → A / xA / xB = A / xB)
52, 4eqtrd 2069 . 2 (A V → A / xA / xB = A / xB)
61, 5syl 14 1 (A 𝑉A / xA / xB = A / xB)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242   wcel 1390  Vcvv 2551  csb 2846
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-sbc 2759  df-csb 2847
This theorem is referenced by: (None)
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