Description: The base set of a constructed one-slot structure. (Contributed by AV, 27-Mar-2020)
Ref | Expression | ||
---|---|---|---|
Hypothesis | 1str.g | ⊢ 𝐺 = { 〈 ( Base ‘ ndx ) , 𝐵 〉 } | |
Assertion | 1strbas | ⊢ ( 𝐵 ∈ 𝑉 → 𝐵 = ( Base ‘ 𝐺 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1str.g | ⊢ 𝐺 = { 〈 ( Base ‘ ndx ) , 𝐵 〉 } | |
2 | 1 | 1strstr | ⊢ 𝐺 Struct 〈 1 , 1 〉 |
3 | baseid | ⊢ Base = Slot ( Base ‘ ndx ) | |
4 | 1 | eqimss2i | ⊢ { 〈 ( Base ‘ ndx ) , 𝐵 〉 } ⊆ 𝐺 |
5 | 2 3 4 | strfv | ⊢ ( 𝐵 ∈ 𝑉 → 𝐵 = ( Base ‘ 𝐺 ) ) |