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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 5074 | . 2 ⊢ ((𝐹:𝐴⟶𝐵 ∧ 𝐵 ⊆ 𝐶) → 𝐹:𝐴⟶𝐶) | |
4 | 1, 2, 3 | syl2anc 403 | 1 ⊢ (𝜑 → 𝐹:𝐴⟶𝐶) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ⊆ wss 2973 ⟶wf 4918 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-in 2979 df-ss 2986 df-f 4926 |
This theorem is referenced by: ac6sfi 6379 fseq1p1m1 9111 resqrexlemcvg 9905 resqrexlemsqa 9910 climcvg1nlem 10186 |
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