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

Theorem nffv 5106
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 x𝐹
nffv.2 xA
Assertion
Ref Expression
nffv x(𝐹A)

Proof of Theorem nffv
Dummy variable y is distinct from all other variables.
StepHypRef Expression
1 df-fv 4833 . 2 (𝐹A) = (℩yA𝐹y)
2 nffv.2 . . . 4 xA
3 nffv.1 . . . 4 x𝐹
4 nfcv 2156 . . . 4 xy
52, 3, 4nfbr 3778 . . 3 x A𝐹y
65nfiotaxy 4794 . 2 x(℩yA𝐹y)
71, 6nfcxfr 2153 1 x(𝐹A)
Colors of variables: wff set class
Syntax hints:  wnfc 2143   class class class wbr 3734  cio 4788  cfv 4825
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 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-3an 873  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-rex 2286  df-v 2533  df-un 2895  df-sn 3352  df-pr 3353  df-op 3355  df-uni 3551  df-br 3735  df-iota 4790  df-fv 4833
This theorem is referenced by:  nffvmpt1  5107  nffvd  5108  dffn5imf  5149  fvmptssdm  5176  fvmptf  5184  eqfnfv2f  5190  ralrnmpt  5230  rexrnmpt  5231  ffnfvf  5245  funiunfvdmf  5324  dff13f  5330  nfiso  5367  nfrecs  5840
  Copyright terms: Public domain W3C validator