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Mirrors > Home > ILE Home > Th. List > nfel1 | GIF version |
Description: Hypothesis builder for elementhood, special case. (Contributed by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
nfeq1.1 | ⊢ Ⅎ𝑥𝐴 |
Ref | Expression |
---|---|
nfel1 | ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfeq1.1 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | nfcv 2178 | . 2 ⊢ Ⅎ𝑥𝐵 | |
3 | 1, 2 | nfel 2186 | 1 ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1349 ∈ wcel 1393 Ⅎwnfc 2165 |
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 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-cleq 2033 df-clel 2036 df-nfc 2167 |
This theorem is referenced by: vtocl2gf 2615 vtocl3gf 2616 vtoclgaf 2618 vtocl2gaf 2620 vtocl3gaf 2622 nfop 3565 pofun 4049 nfse 4078 rabxfrd 4201 mptfvex 5256 fvmptf 5263 fmptcof 5331 fliftfuns 5438 riota2f 5489 ovmpt2s 5624 ov2gf 5625 fmpt2x 5826 mpt2fvex 5829 qliftfuns 6190 |
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