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Mirrors > Home > ILE Home > Th. List > issetri | GIF version |
Description: A way to say "𝐴 is a set" (inference form). (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
issetri.1 | ⊢ ∃𝑥 𝑥 = 𝐴 |
Ref | Expression |
---|---|
issetri | ⊢ 𝐴 ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | issetri.1 | . 2 ⊢ ∃𝑥 𝑥 = 𝐴 | |
2 | isset 2692 | . 2 ⊢ (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | mpbir 145 | 1 ⊢ 𝐴 ∈ V |
Colors of variables: wff set class |
Syntax hints: = wceq 1331 ∃wex 1468 ∈ wcel 1480 Vcvv 2686 |
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 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-v 2688 |
This theorem is referenced by: 0ex 4055 inex1 4062 vpwex 4103 zfpair2 4132 uniex 4359 bdinex1 13097 bj-zfpair2 13108 bj-uniex 13115 bj-omex2 13175 |
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