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Theorem csbconstgf 2863
 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 2862 . 2 ((𝐴𝑉𝑥𝐵) → 𝐴 / 𝑥𝐵 = 𝐵)
31, 2mpan2 401 1 (𝐴𝑉𝐴 / 𝑥𝐵 = 𝐵)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1243   ∈ wcel 1393  Ⅎwnfc 2165  ⦋csb 2852 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-sbc 2765  df-csb 2853 This theorem is referenced by:  csbconstg  2864
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