Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > frexr | Structured version Visualization version GIF version |
Description: A function taking real values, is a function taking extended real values. Common case. (Contributed by Glauco Siliprandi, 26-Jun-2021.) |
Ref | Expression |
---|---|
frexr.1 | ⊢ (𝜑 → 𝐹:𝐴⟶ℝ) |
Ref | Expression |
---|---|
frexr | ⊢ (𝜑 → 𝐹:𝐴⟶ℝ*) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frexr.1 | . 2 ⊢ (𝜑 → 𝐹:𝐴⟶ℝ) | |
2 | ressxr 9962 | . . 3 ⊢ ℝ ⊆ ℝ* | |
3 | 2 | a1i 11 | . 2 ⊢ (𝜑 → ℝ ⊆ ℝ*) |
4 | 1, 3 | fssd 5970 | 1 ⊢ (𝜑 → 𝐹:𝐴⟶ℝ*) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ⊆ wss 3540 ⟶wf 5800 ℝcr 9814 ℝ*cxr 9952 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-un 3545 df-in 3547 df-ss 3554 df-f 5808 df-xr 9957 |
This theorem is referenced by: preimaioomnf 39606 issmfltle 39622 incsmf 39629 issmfle 39632 decsmf 39653 |
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