Description: Derive Axiom ax-his1 from Hilbert space under ZF set theory. (Contributed by NM, 31-May-2008) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | axhil.1 | |
|
axhil.2 | |
||
axhfi.1 | |
||
Assertion | axhis1-zf | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axhil.1 | |
|
2 | axhil.2 | |
|
3 | axhfi.1 | |
|
4 | df-hba | |
|
5 | 1 | fveq2i | |
6 | 4 5 | eqtr4i | |
7 | 6 3 | hlipcj | |
8 | 2 7 | mp3an1 | |