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

Theorem nffv 5128
Description: Bound-variable hypothesis builder for function value. (Contributed by NM, 14-Nov-1995.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
nffv.1  F/_ F
nffv.2  F/_
Assertion
Ref Expression
nffv  F/_ F `

Proof of Theorem nffv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-fv 4853 . 2  F `
 iota F
2 nffv.2 . . . 4  F/_
3 nffv.1 . . . 4  F/_ F
4 nfcv 2175 . . . 4  F/_
52, 3, 4nfbr 3799 . . 3  F/  F
65nfiotaxy 4814 . 2  F/_ iota F
71, 6nfcxfr 2172 1  F/_ F `
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2162   class class class wbr 3755   iotacio 4808   ` cfv 4845
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-un 2916  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-iota 4810  df-fv 4853
This theorem is referenced by:  nffvmpt1  5129  nffvd  5130  dffn5imf  5171  fvmptssdm  5198  fvmptf  5206  eqfnfv2f  5212  ralrnmpt  5252  rexrnmpt  5253  ffnfvf  5267  funiunfvdmf  5346  dff13f  5352  nfiso  5389  nfrecs  5863  nffrec  5921  nfiseq  8898
  Copyright terms: Public domain W3C validator