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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 3453 | . 2 ⊢ (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | mpbir 234 | 1 ⊢ 𝐴 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1538 ∃wex 1781 ∈ wcel 2111 Vcvv 3441 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1782 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-v 3443 |
This theorem is referenced by: zfrep4 5164 0ex 5175 inex1 5185 vpwex 5243 zfpair2 5296 vuniex 7445 bj-snsetex 34399 |
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