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Theorem csbconstgf 3511
Description: Substitution doesn't affect a constant 𝐵 (in which 𝑥 is not free). (Contributed by NM, 10-Nov-2005.)
Hypothesis
Ref Expression
csbconstgf.1 𝑥𝐵
Assertion
Ref Expression
csbconstgf (𝐴𝑉𝐴 / 𝑥𝐵 = 𝐵)

Proof of Theorem csbconstgf
StepHypRef Expression
1 csbconstgf.1 . 2 𝑥𝐵
2 csbtt 3510 . 2 ((𝐴𝑉𝑥𝐵) → 𝐴 / 𝑥𝐵 = 𝐵)
31, 2mpan2 703 1 (𝐴𝑉𝐴 / 𝑥𝐵 = 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1475  wcel 1977  wnfc 2738  csb 3499
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-sbc 3403  df-csb 3500
This theorem is referenced by:  csbconstg  3512  fmptdF  28630  poimirlem25  32398
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