![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > mpteq2i | GIF version |
Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 16-Dec-2013.) |
Ref | Expression |
---|---|
mpteq2i.1 | ⊢ 𝐵 = 𝐶 |
Ref | Expression |
---|---|
mpteq2i | ⊢ (𝑥 ∈ 𝐴 ↦ 𝐵) = (𝑥 ∈ 𝐴 ↦ 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpteq2i.1 | . . 3 ⊢ 𝐵 = 𝐶 | |
2 | 1 | a1i 9 | . 2 ⊢ (𝑥 ∈ 𝐴 → 𝐵 = 𝐶) |
3 | 2 | mpteq2ia 4022 | 1 ⊢ (𝑥 ∈ 𝐴 ↦ 𝐵) = (𝑥 ∈ 𝐴 ↦ 𝐶) |
Colors of variables: wff set class |
Syntax hints: = wceq 1332 ∈ wcel 1481 ↦ cmpt 3997 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-ral 2422 df-opab 3998 df-mpt 3999 |
This theorem is referenced by: frecsuc 6312 fodjuomni 7029 fodjumkv 7042 axcaucvg 7732 0tonninf 10243 1tonninf 10244 cbvsum 11161 cbvprod 11359 eirraplem 11519 cnmpt12f 12494 fsumcncntop 12764 dvef 12896 nninfsellemqall 13386 nninfomni 13390 exmidsbthr 13393 |
Copyright terms: Public domain | W3C validator |