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Theorem csbfv2g 5153
Description: Move class substitution in and out of a function value. (Contributed by NM, 10-Nov-2005.)
Assertion
Ref Expression
csbfv2g (A 𝐶A / x(𝐹B) = (𝐹A / xB))
Distinct variable group:   x,𝐹
Allowed substitution hints:   A(x)   B(x)   𝐶(x)

Proof of Theorem csbfv2g
StepHypRef Expression
1 csbfv12g 5152 . 2 (A 𝐶A / x(𝐹B) = (A / x𝐹A / xB))
2 csbconstg 2858 . . 3 (A 𝐶A / x𝐹 = 𝐹)
32fveq1d 5123 . 2 (A 𝐶 → (A / x𝐹A / xB) = (𝐹A / xB))
41, 3eqtrd 2069 1 (A 𝐶A / x(𝐹B) = (𝐹A / xB))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1242   wcel 1390  csb 2846  cfv 4845
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-rex 2306  df-v 2553  df-sbc 2759  df-csb 2847  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853
This theorem is referenced by:  csbfvg  5154
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