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Theorem csbconstgf 2986
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 2985 . 2 ((𝐴𝑉𝑥𝐵) → 𝐴 / 𝑥𝐵 = 𝐵)
31, 2mpan2 421 1 (𝐴𝑉𝐴 / 𝑥𝐵 = 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1316  wcel 1465  wnfc 2245  csb 2975
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-sbc 2883  df-csb 2976
This theorem is referenced by:  csbconstg  2987
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