Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfeq2 GIF version

Theorem nfeq2 2293
 Description: Hypothesis builder for equality, special case. (Contributed by Mario Carneiro, 10-Oct-2016.)
Hypothesis
Ref Expression
nfeq2.1 𝑥𝐵
Assertion
Ref Expression
nfeq2 𝑥 𝐴 = 𝐵
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝐵(𝑥)

Proof of Theorem nfeq2
StepHypRef Expression
1 nfcv 2281 . 2 𝑥𝐴
2 nfeq2.1 . 2 𝑥𝐵
31, 2nfeq 2289 1 𝑥 𝐴 = 𝐵
 Colors of variables: wff set class Syntax hints:   = wceq 1331  Ⅎwnf 1436  Ⅎwnfc 2268 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-cleq 2132  df-clel 2135  df-nfc 2270 This theorem is referenced by:  issetf  2693  eqvincf  2810  csbhypf  3038  nfpr  3573  intab  3800  nfmpt  4020  cbvmptf  4022  cbvmpt  4023  repizf2  4086  moop2  4173  eusvnf  4374  elrnmpt1  4790  fmptco  5586  elabrex  5659  nfmpo  5840  cbvmpox  5849  ovmpodxf  5896  fmpox  6098  f1od2  6132  nfrecs  6204  erovlem  6521  xpf1o  6738  mapxpen  6742  mkvprop  7032  lble  8705  nfsum1  11125  nfsum  11126  zsumdc  11153  fsum3  11156  fsum3cvg2  11163  fsum2dlemstep  11203  mertenslem2  11305  nfcprod1  11323  nfcprod  11324  ctiunctlemfo  11952  ellimc3apf  12798
 Copyright terms: Public domain W3C validator