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 4014 | 1 ⊢ (𝑥 ∈ 𝐴 ↦ 𝐵) = (𝑥 ∈ 𝐴 ↦ 𝐶) |
Colors of variables: wff set class |
Syntax hints: = wceq 1331 ∈ wcel 1480 ↦ cmpt 3989 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-ral 2421 df-opab 3990 df-mpt 3991 |
This theorem is referenced by: frecsuc 6304 fodjuomni 7021 fodjumkv 7034 axcaucvg 7708 0tonninf 10212 1tonninf 10213 cbvsum 11129 cbvprod 11327 eirraplem 11483 cnmpt12f 12455 fsumcncntop 12725 dvef 12856 nninfsellemqall 13211 nninfomni 13215 exmidsbthr 13218 |
Copyright terms: Public domain | W3C validator |