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Mirrors > Home > ILE Home > Th. List > isseti | GIF version |
Description: A way to say "𝐴 is a set" (inference form). (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 2736 | . 2 ⊢ (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | mpbi 144 | 1 ⊢ ∃𝑥 𝑥 = 𝐴 |
Colors of variables: wff set class |
Syntax hints: = wceq 1348 ∃wex 1485 ∈ wcel 2141 Vcvv 2730 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-v 2732 |
This theorem is referenced by: rexcom4b 2755 ceqsex 2768 vtoclf 2783 vtocl2 2785 vtocl3 2786 vtoclef 2803 eqvinc 2853 euind 2917 opabm 4263 eusv2nf 4439 dtruex 4541 limom 4596 isarep2 5283 dfoprab2 5897 rnoprab 5933 dmaddpq 7328 dmmulpq 7329 bj-inf2vnlem1 13927 |
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