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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 2758 | . 2 ⊢ (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | mpbir 146 | 1 ⊢ 𝐴 ∈ V |
Colors of variables: wff set class |
Syntax hints: = wceq 1364 ∃wex 1503 ∈ wcel 2160 Vcvv 2752 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-v 2754 |
This theorem is referenced by: 0ex 4145 inex1 4152 vpwex 4197 zfpair2 4228 uniex 4455 bdinex1 15112 bj-zfpair2 15123 bj-uniex 15130 bj-omex2 15190 |
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