![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > elisset | GIF version |
Description: An element of a class exists. (Contributed by NM, 1-May-1995.) |
Ref | Expression |
---|---|
elisset | ⊢ (A ∈ 𝑉 → ∃x x = A) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2560 | . 2 ⊢ (A ∈ 𝑉 → A ∈ V) | |
2 | isset 2555 | . 2 ⊢ (A ∈ V ↔ ∃x x = A) | |
3 | 1, 2 | sylib 127 | 1 ⊢ (A ∈ 𝑉 → ∃x x = A) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1242 ∃wex 1378 ∈ wcel 1390 Vcvv 2551 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-v 2553 |
This theorem is referenced by: elex22 2563 elex2 2564 ceqsalt 2574 ceqsalg 2576 cgsexg 2583 cgsex2g 2584 cgsex4g 2585 vtoclgft 2598 vtocleg 2618 vtoclegft 2619 spc2egv 2636 spc2gv 2637 spc3egv 2638 spc3gv 2639 eqvincg 2662 tpid3g 3474 iinexgm 3899 copsex2t 3973 copsex2g 3974 ralxfr2d 4162 rexxfr2d 4163 fliftf 5382 eloprabga 5533 ovmpt4g 5565 eroveu 6133 genpassl 6507 genpassu 6508 nn1suc 7714 bj-inex 9362 |
Copyright terms: Public domain | W3C validator |