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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 2736 | . 2 ⊢ (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | mpbir 145 | 1 ⊢ 𝐴 ∈ V |
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: 0ex 4114 inex1 4121 vpwex 4163 zfpair2 4193 uniex 4420 bdinex1 13899 bj-zfpair2 13910 bj-uniex 13917 bj-omex2 13977 |
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