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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 3946 | 1 ⊢ (𝑥 ∈ 𝐴 ↦ 𝐵) = (𝑥 ∈ 𝐴 ↦ 𝐶) |
Colors of variables: wff set class |
Syntax hints: = wceq 1296 ∈ wcel 1445 ↦ cmpt 3921 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-11 1449 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-ral 2375 df-opab 3922 df-mpt 3923 |
This theorem is referenced by: frecsuc 6210 fodjuomni 6892 fodjumkv 6903 axcaucvg 7532 0tonninf 9994 1tonninf 9995 cbvsum 10903 eirraplem 11213 nninfsellemqall 12621 nninfomni 12625 exmidsbthr 12627 |
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