![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 3486 | . 2 ⊢ (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | mpbir 230 | 1 ⊢ 𝐴 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 ∃wex 1773 ∈ wcel 2098 Vcvv 3473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2699 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2706 df-cleq 2720 df-clel 2806 df-v 3475 |
This theorem is referenced by: zfrep4 5300 0ex 5311 inex1 5321 vpwex 5381 zfpair2 5434 vuniex 7750 bj-snsetex 36475 |
Copyright terms: Public domain | W3C validator |