ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  csbconstgf Unicode version

Theorem csbconstgf 3062
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 3061 . 2  |-  ( ( A  e.  V  /\  F/_ x B )  ->  [_ A  /  x ]_ B  =  B
)
31, 2mpan2 423 1  |-  ( A  e.  V  ->  [_ A  /  x ]_ B  =  B )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1348    e. wcel 2141   F/_wnfc 2299   [_csb 3049
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-sbc 2956  df-csb 3050
This theorem is referenced by:  csbconstg  3063
  Copyright terms: Public domain W3C validator