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

Theorem nfcxfrd 2317
Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypotheses
Ref Expression
nfceqi.1  |-  A  =  B
nfcxfrd.2  |-  ( ph  -> 
F/_ x B )
Assertion
Ref Expression
nfcxfrd  |-  ( ph  -> 
F/_ x A )

Proof of Theorem nfcxfrd
StepHypRef Expression
1 nfcxfrd.2 . 2  |-  ( ph  -> 
F/_ x B )
2 nfceqi.1 . . 3  |-  A  =  B
32nfceqi 2315 . 2  |-  ( F/_ x A  <->  F/_ x B )
41, 3sylibr 134 1  |-  ( ph  -> 
F/_ x A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1353   F/_wnfc 2306
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-cleq 2170  df-clel 2173  df-nfc 2308
This theorem is referenced by:  nfcsb1d  3088  nfcsbd  3092  nfcsbw  3093  nfifd  3561  nfunid  3816  nfiotadw  5181  nfriotadxy  5838  nfovd  5903  nfnegd  8151
  Copyright terms: Public domain W3C validator