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Mirrors > Home > ILE Home > Th. List > nfel2 | GIF version |
Description: Hypothesis builder for elementhood, special case. (Contributed by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
nfeq2.1 | ⊢ Ⅎ𝑥𝐵 |
Ref | Expression |
---|---|
nfel2 | ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2235 | . 2 ⊢ Ⅎ𝑥𝐴 | |
2 | nfeq2.1 | . 2 ⊢ Ⅎ𝑥𝐵 | |
3 | 1, 2 | nfel 2244 | 1 ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnf 1401 ∈ wcel 1445 Ⅎwnfc 2222 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-tru 1299 df-nf 1402 df-sb 1700 df-cleq 2088 df-clel 2091 df-nfc 2224 |
This theorem is referenced by: elabgt 2771 opelopabsb 4111 eliunxp 4606 opeliunxp2 4607 tz6.12f 5368 0neqopab 5732 disjxp1 6039 opeliunxp2f 6041 cbvixp 6512 |
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