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Theorem csbconstgf 3094
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 3093 . 2  |-  ( ( A  e.  V  /\  F/_ x B )  ->  [_ A  /  x ]_ B  =  B
)
31, 2mpan2 652 1  |-  ( A  e.  V  ->  [_ A  /  x ]_ B  =  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623    e. wcel 1684   F/_wnfc 2406   [_csb 3081
This theorem is referenced by:  csbconstg  3095  fmptdF  23221
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-sbc 2992  df-csb 3082
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