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Theorem csbconstgf 3149
 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 (A V[A / x]B = B)

Proof of Theorem csbconstgf
StepHypRef Expression
1 csbconstgf.1 . 2 xB
2 csbtt 3148 . 2 ((A V xB) → [A / x]B = B)
31, 2mpan2 652 1 (A V[A / x]B = B)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   ∈ wcel 1710  Ⅎwnfc 2476  [csb 3136 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047  df-csb 3137 This theorem is referenced by:  csbconstg  3150
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