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Mirrors > Home > MPE Home > Th. List > mpteq1iOLD | Structured version Visualization version GIF version |
Description: An equality theorem for the maps-to notation. (Contributed by Glauco Siliprandi, 17-Aug-2020.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
mpteq1i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
mpteq1iOLD | ⊢ (𝑥 ∈ 𝐴 ↦ 𝐶) = (𝑥 ∈ 𝐵 ↦ 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpteq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | mpteq1 5202 | . 2 ⊢ (𝐴 = 𝐵 → (𝑥 ∈ 𝐴 ↦ 𝐶) = (𝑥 ∈ 𝐵 ↦ 𝐶)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝑥 ∈ 𝐴 ↦ 𝐶) = (𝑥 ∈ 𝐵 ↦ 𝐶) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ↦ cmpt 5192 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-opab 5172 df-mpt 5193 |
This theorem is referenced by: (None) |
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