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

Theorem nffv 5213
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/_ x F
nffv.2  |-  F/_ x A
Assertion
Ref Expression
nffv  |-  F/_ x
( F `  A
)

Proof of Theorem nffv
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 df-fv 4938 . 2  |-  ( F `
 A )  =  ( iota y A F y )
2 nffv.2 . . . 4  |-  F/_ x A
3 nffv.1 . . . 4  |-  F/_ x F
4 nfcv 2194 . . . 4  |-  F/_ x
y
52, 3, 4nfbr 3836 . . 3  |-  F/ x  A F y
65nfiotaxy 4899 . 2  |-  F/_ x
( iota y A F y )
71, 6nfcxfr 2191 1  |-  F/_ x
( F `  A
)
Colors of variables: wff set class
Syntax hints:   F/_wnfc 2181   class class class wbr 3792   iotacio 4893   ` cfv 4930
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rex 2329  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410  df-op 3412  df-uni 3609  df-br 3793  df-iota 4895  df-fv 4938
This theorem is referenced by:  nffvmpt1  5214  nffvd  5215  dffn5imf  5256  fvmptssdm  5283  fvmptf  5291  eqfnfv2f  5297  ralrnmpt  5337  rexrnmpt  5338  ffnfvf  5352  funiunfvdmf  5431  dff13f  5437  nfiso  5474  nfrecs  5953  nffrec  6013  nfiseq  9382  nfsum1  10106  nfsum  10107
  Copyright terms: Public domain W3C validator