ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nfel1 Structured version   GIF version

Theorem nfel1 2185
Description: Hypothesis builder for elementhood, special case. (Contributed by Mario Carneiro, 10-Oct-2016.)
Hypothesis
Ref Expression
nfeq1.1 xA
Assertion
Ref Expression
nfel1 x A B
Distinct variable group:   x,B
Allowed substitution hint:   A(x)

Proof of Theorem nfel1
StepHypRef Expression
1 nfeq1.1 . 2 xA
2 nfcv 2175 . 2 xB
31, 2nfel 2183 1 x A B
Colors of variables: wff set class
Syntax hints:  wnf 1346   wcel 1390  wnfc 2162
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-bnd 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-tru 1245  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164
This theorem is referenced by:  vtocl2gf  2609  vtocl3gf  2610  vtoclgaf  2612  vtocl2gaf  2614  vtocl3gaf  2616  nfop  3556  pofun  4040  nfse  4063  rabxfrd  4167  mptfvex  5199  fvmptf  5206  fmptcof  5274  fliftfuns  5381  riota2f  5432  ovmpt2s  5566  ov2gf  5567  fmpt2x  5768  mpt2fvex  5771  qliftfuns  6126
  Copyright terms: Public domain W3C validator