Description: The other slot of a constructed two-slot structure. (Contributed by Mario Carneiro, 29-Aug-2015) Use the index-independent version 2strop1 instead. (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | 2str.g | ⊢ 𝐺 = { 〈 ( Base ‘ ndx ) , 𝐵 〉 , 〈 ( 𝐸 ‘ ndx ) , + 〉 } | |
2str.e | ⊢ 𝐸 = Slot 𝑁 | ||
2str.l | ⊢ 1 < 𝑁 | ||
2str.n | ⊢ 𝑁 ∈ ℕ | ||
Assertion | 2strop | ⊢ ( + ∈ 𝑉 → + = ( 𝐸 ‘ 𝐺 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2str.g | ⊢ 𝐺 = { 〈 ( Base ‘ ndx ) , 𝐵 〉 , 〈 ( 𝐸 ‘ ndx ) , + 〉 } | |
2 | 2str.e | ⊢ 𝐸 = Slot 𝑁 | |
3 | 2str.l | ⊢ 1 < 𝑁 | |
4 | 2str.n | ⊢ 𝑁 ∈ ℕ | |
5 | 1 2 3 4 | 2strstr | ⊢ 𝐺 Struct 〈 1 , 𝑁 〉 |
6 | 2 4 | ndxid | ⊢ 𝐸 = Slot ( 𝐸 ‘ ndx ) |
7 | snsspr2 | ⊢ { 〈 ( 𝐸 ‘ ndx ) , + 〉 } ⊆ { 〈 ( Base ‘ ndx ) , 𝐵 〉 , 〈 ( 𝐸 ‘ ndx ) , + 〉 } | |
8 | 7 1 | sseqtrri | ⊢ { 〈 ( 𝐸 ‘ ndx ) , + 〉 } ⊆ 𝐺 |
9 | 5 6 8 | strfv | ⊢ ( + ∈ 𝑉 → + = ( 𝐸 ‘ 𝐺 ) ) |