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

Theorem nfralxy 2528
Description: Old name for nfralw 2527. (Contributed by Jim Kingdon, 30-May-2018.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfralxy.1  |-  F/_ x A
nfralxy.2  |-  F/ x ph
Assertion
Ref Expression
nfralxy  |-  F/ x A. y  e.  A  ph
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)    A( x, y)

Proof of Theorem nfralxy
StepHypRef Expression
1 nftru 1477 . . 3  |-  F/ y T.
2 nfralxy.1 . . . 4  |-  F/_ x A
32a1i 9 . . 3  |-  ( T. 
->  F/_ x A )
4 nfralxy.2 . . . 4  |-  F/ x ph
54a1i 9 . . 3  |-  ( T. 
->  F/ x ph )
61, 3, 5nfraldxy 2523 . 2  |-  ( T. 
->  F/ x A. y  e.  A  ph )
76mptru 1373 1  |-  F/ x A. y  e.  A  ph
Colors of variables: wff set class
Syntax hints:   T. wtru 1365   F/wnf 1471   F/_wnfc 2319   A.wral 2468
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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473
This theorem is referenced by:  nfra2xy  2532  rspc2  2867  sbcralt  3054  sbcralg  3056  raaanlem  3543  nfint  3869  nfiinxy  3928  nfpo  4319  nfso  4320  nfse  4359  nffrfor  4366  nfwe  4373  ralxpf  4791  funimaexglem  5318  fun11iun  5501  dff13f  5792  nfiso  5828  mpoeq123  5956  nfofr  6114  fmpox  6226  nfrecs  6333  xpf1o  6873  ac6sfi  6927  ismkvnex  7184  lble  8935  fzrevral  10137  nfsum1  11399  nfsum  11400  fsum2dlemstep  11477  fisumcom2  11481  nfcprod1  11597  nfcprod  11598  bezoutlemmain  12034  cnmpt21  14268  setindis  15197  bdsetindis  15199  strcollnfALT  15216  isomninnlem  15257  iswomninnlem  15276  ismkvnnlem  15279
  Copyright terms: Public domain W3C validator