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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 rule). (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 3347 | . 2 ⊢ (𝐴 ∈ V ↔ ∃𝑥 𝑥 = 𝐴) | |
3 | 1, 2 | mpbir 221 | 1 ⊢ 𝐴 ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1632 ∃wex 1853 ∈ wcel 2139 Vcvv 3340 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1871 ax-4 1886 ax-5 1988 ax-6 2054 ax-7 2090 ax-9 2148 ax-12 2196 ax-ext 2740 |
This theorem depends on definitions: df-bi 197 df-an 385 df-tru 1635 df-ex 1854 df-sb 2047 df-clab 2747 df-cleq 2753 df-clel 2756 df-v 3342 |
This theorem is referenced by: zfrep4 4931 0ex 4942 inex1 4951 pwex 4997 zfpair2 5056 uniex 7119 bj-snsetex 33275 |
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