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Mirrors > Home > MPE Home > Th. List > issetri | Structured version Visualization version GIF version |
Description: A way to say "𝐴 is a set" (inference form). (Contributed by NM, 21-Jun-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 3436 | . 2 ⊢ (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | mpbir 234 | 1 ⊢ 𝐴 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1543 ∃wex 1787 ∈ wcel 2112 Vcvv 3423 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2114 ax-9 2122 ax-ext 2710 |
This theorem depends on definitions: df-bi 210 df-an 400 df-tru 1546 df-ex 1788 df-sb 2073 df-clab 2717 df-cleq 2731 df-clel 2818 df-v 3425 |
This theorem is referenced by: zfrep4 5206 0ex 5217 inex1 5227 vpwex 5287 zfpair2 5340 vuniex 7549 bj-snsetex 34924 |
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