New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > issetf | GIF version |
Description: A version of isset that does not require x and A to be distinct. (Contributed by Andrew Salmon, 6-Jun-2011.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
issetf.1 | ⊢ ℲxA |
Ref | Expression |
---|---|
issetf | ⊢ (A ∈ V ↔ ∃x x = A) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isset 2863 | . 2 ⊢ (A ∈ V ↔ ∃y y = A) | |
2 | issetf.1 | . . . 4 ⊢ ℲxA | |
3 | 2 | nfeq2 2500 | . . 3 ⊢ Ⅎx y = A |
4 | nfv 1619 | . . 3 ⊢ Ⅎy x = A | |
5 | eqeq1 2359 | . . 3 ⊢ (y = x → (y = A ↔ x = A)) | |
6 | 3, 4, 5 | cbvex 1985 | . 2 ⊢ (∃y y = A ↔ ∃x x = A) |
7 | 1, 6 | bitri 240 | 1 ⊢ (A ∈ V ↔ ∃x x = A) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 176 ∃wex 1541 = wceq 1642 ∈ wcel 1710 Ⅎwnfc 2476 Vcvv 2859 |
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-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 |
This theorem is referenced by: vtoclgf 2913 spcimgft 2930 |
Copyright terms: Public domain | W3C validator |