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Theorem csbconstgf 3264
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  |-  F/_ x B
Assertion
Ref Expression
csbconstgf  |-  ( A  e.  V  ->  [_ A  /  x ]_ B  =  B )

Proof of Theorem csbconstgf
StepHypRef Expression
1 csbconstgf.1 . 2  |-  F/_ x B
2 csbtt 3263 . 2  |-  ( ( A  e.  V  /\  F/_ x B )  ->  [_ A  /  x ]_ B  =  B
)
31, 2mpan2 653 1  |-  ( A  e.  V  ->  [_ A  /  x ]_ B  =  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652    e. wcel 1725   F/_wnfc 2559   [_csb 3251
This theorem is referenced by:  csbconstg  3265  fmptdF  24069
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-sbc 3162  df-csb 3252
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