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Theorem csbconstgf 3740
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 3739 . 2 ((𝐴𝑉𝑥𝐵) → 𝐴 / 𝑥𝐵 = 𝐵)
31, 2mpan2 674 1 (𝐴𝑉𝐴 / 𝑥𝐵 = 𝐵)
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1637  wcel 2156  wnfc 2935  csb 3728
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2068  ax-7 2104  ax-9 2165  ax-10 2185  ax-11 2201  ax-12 2214  ax-13 2420  ax-ext 2784
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2061  df-clab 2793  df-cleq 2799  df-clel 2802  df-nfc 2937  df-v 3393  df-sbc 3634  df-csb 3729
This theorem is referenced by:  csbconstg  3741  fmptdF  29783  poimirlem25  33747
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