Theorem nfel1 2229

Description: Hypothesis builder for elementhood, special case. (Contributed by Mario Carneiro, 10-Oct-2016.)

Hypothesis

Ref	Expression
nfeq1.1	⊢ Ⅎ𝑥𝐴

Assertion

Ref	Expression
nfel1	⊢ Ⅎ𝑥 𝐴 ∈ 𝐵

Distinct variable group:   𝑥,𝐵

Allowed substitution hint:   𝐴(𝑥)

Proof of Theorem nfel1

Step	Hyp	Ref	Expression
1		nfeq1.1	. 2 ⊢ Ⅎ𝑥𝐴
2		nfcv 2219	. 2 ⊢ Ⅎ𝑥𝐵
3	1, 2	nfel 2227	1 ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵

Syntax hints:  Ⅎwnf 1389   ∈ wcel 1433  Ⅎwnfc 2206

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-cleq 2074  df-clel 2077  df-nfc 2208

This theorem is referenced by:  vtocl2gf  2660  vtocl3gf  2661  vtoclgaf  2663  vtocl2gaf  2665  vtocl3gaf  2667  nfop  3586  pofun  4067  nfse  4096  rabxfrd  4219  mptfvex  5277  fvmptf  5284  fmptcof  5352  fliftfuns  5458  riota2f  5509  ovmpt2s  5644  ov2gf  5645  fmpt2x  5846  mpt2fvex  5849  qliftfuns  6213  infssuzcldc  10347