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Mirrors > Home > NFE Home > Th. List > isseti | GIF version |
Description: A way to say "A is a set" (inference rule). (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
isseti.1 | ⊢ A ∈ V |
Ref | Expression |
---|---|
isseti | ⊢ ∃x x = A |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isseti.1 | . 2 ⊢ A ∈ V | |
2 | isset 2864 | . 2 ⊢ (A ∈ V ↔ ∃x x = A) | |
3 | 1, 2 | mpbi 199 | 1 ⊢ ∃x x = A |
Colors of variables: wff setvar class |
Syntax hints: ∃wex 1541 = wceq 1642 ∈ wcel 1710 Vcvv 2860 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-v 2862 |
This theorem is referenced by: rexcom4b 2881 ceqsex 2894 vtoclf 2909 vtocl2 2911 vtocl3 2912 vtoclef 2928 eqvinc 2967 euind 3024 opabn0 4717 dmsi 5520 rnoprab 5577 ov3 5600 dmtxp 5803 dmpprod 5841 |
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