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Mirrors > Home > ILE Home > Th. List > isseti | GIF version |
Description: A way to say "𝐴 is a set" (inference rule). (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
isseti.1 | ⊢ 𝐴 ∈ V |
Ref | Expression |
---|---|
isseti | ⊢ ∃𝑥 𝑥 = 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isseti.1 | . 2 ⊢ 𝐴 ∈ V | |
2 | isset 2605 | . 2 ⊢ (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | mpbi 143 | 1 ⊢ ∃𝑥 𝑥 = 𝐴 |
Colors of variables: wff set class |
Syntax hints: = wceq 1284 ∃wex 1421 ∈ wcel 1433 Vcvv 2601 |
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-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-v 2603 |
This theorem is referenced by: rexcom4b 2624 ceqsex 2637 vtoclf 2652 vtocl2 2654 vtocl3 2655 vtoclef 2671 eqvinc 2718 euind 2779 opabm 4035 eusv2nf 4206 dtruex 4302 limom 4354 isarep2 5006 dfoprab2 5572 rnoprab 5607 dmaddpq 6569 dmmulpq 6570 bj-inf2vnlem1 10765 |
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