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Mirrors > Home > ILE Home > Th. List > fssd | GIF version |
Description: Expanding the codomain of a mapping, deduction form. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
fssd.f | ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) |
fssd.b | ⊢ (𝜑 → 𝐵 ⊆ 𝐶) |
Ref | Expression |
---|---|
fssd | ⊢ (𝜑 → 𝐹:𝐴⟶𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fssd.f | . 2 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) | |
2 | fssd.b | . 2 ⊢ (𝜑 → 𝐵 ⊆ 𝐶) | |
3 | fss 5379 | . 2 ⊢ ((𝐹:𝐴⟶𝐵 ∧ 𝐵 ⊆ 𝐶) → 𝐹:𝐴⟶𝐶) | |
4 | 1, 2, 3 | syl2anc 411 | 1 ⊢ (𝜑 → 𝐹:𝐴⟶𝐶) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ⊆ wss 3131 ⟶wf 5214 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-in 3137 df-ss 3144 df-f 5222 |
This theorem is referenced by: mapss 6693 ac6sfi 6900 fseq1p1m1 10096 resqrexlemcvg 11030 resqrexlemsqa 11035 climcvg1nlem 11359 fsumcl2lem 11408 ennnfonelemh 12407 cnrest2 13775 cnptoprest2 13779 cncfss 14109 limccnpcntop 14183 dvcoapbr 14210 dvef 14227 isomninnlem 14817 trilpolemisumle 14825 iswomninnlem 14836 ismkvnnlem 14839 |
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