![]() |
Hilbert Space Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > HSE Home > Th. List > axhilex-zf | Structured version Visualization version GIF version |
Description: Derive Axiom ax-hilex 31028 from Hilbert space under ZF set theory. (Contributed by NM, 31-May-2008.) (New usage is discouraged.) |
Ref | Expression |
---|---|
axhil.1 | ⊢ 𝑈 = 〈〈 +ℎ , ·ℎ 〉, normℎ〉 |
axhil.2 | ⊢ 𝑈 ∈ CHilOLD |
Ref | Expression |
---|---|
axhilex-zf | ⊢ ℋ ∈ V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-hba 30998 | . 2 ⊢ ℋ = (BaseSet‘〈〈 +ℎ , ·ℎ 〉, normℎ〉) | |
2 | 1 | hlex 30927 | 1 ⊢ ℋ ∈ V |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ∈ wcel 2106 Vcvv 3478 〈cop 4637 CHilOLDchlo 30914 ℋchba 30948 +ℎ cva 30949 ·ℎ csm 30950 normℎcno 30952 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 ax-nul 5312 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1540 df-fal 1550 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-ne 2939 df-v 3480 df-dif 3966 df-un 3968 df-ss 3980 df-nul 4340 df-sn 4632 df-pr 4634 df-uni 4913 df-iota 6516 df-fv 6571 df-hba 30998 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |