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Theorem csbconstgf 3082
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 3081 . 2 ((𝐴𝑉𝑥𝐵) → 𝐴 / 𝑥𝐵 = 𝐵)
31, 2mpan2 425 1 (𝐴𝑉𝐴 / 𝑥𝐵 = 𝐵)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1363  wcel 2158  wnfc 2316  csb 3069
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-sbc 2975  df-csb 3070
This theorem is referenced by:  csbconstg  3083
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