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

Theorem nfralya 2412
Description: Not-free for restricted universal quantification where  y and  A are distinct. See nfralxy 2410 for a version with  x and  y distinct instead. (Contributed by Jim Kingdon, 3-Jun-2018.)
Hypotheses
Ref Expression
nfralya.1  |-  F/_ x A
nfralya.2  |-  F/ x ph
Assertion
Ref Expression
nfralya  |-  F/ x A. y  e.  A  ph
Distinct variable group:    y, A
Allowed substitution hints:    ph( x, y)    A( x)

Proof of Theorem nfralya
StepHypRef Expression
1 nftru 1398 . . 3  |-  F/ y T.
2 nfralya.1 . . . 4  |-  F/_ x A
32a1i 9 . . 3  |-  ( T. 
->  F/_ x A )
4 nfralya.2 . . . 4  |-  F/ x ph
54a1i 9 . . 3  |-  ( T. 
->  F/ x ph )
61, 3, 5nfraldya 2408 . 2  |-  ( T. 
->  F/ x A. y  e.  A  ph )
76trud 1296 1  |-  F/ x A. y  e.  A  ph
Colors of variables: wff set class
Syntax hints:   T. wtru 1288   F/wnf 1392   F/_wnfc 2212   A.wral 2355
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ral 2360
This theorem is referenced by:  nfiinya  3742  nfsup  6631  caucvgsrlemgt1  7284  supinfneg  9015  infsupneg  9016
  Copyright terms: Public domain W3C validator