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Mirrors > Home > ILE Home > Th. List > ssidd | GIF version |
Description: Weakening of ssid 3087. (Contributed by BJ, 1-Sep-2022.) |
Ref | Expression |
---|---|
ssidd | ⊢ (𝜑 → 𝐴 ⊆ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid 3087 | . 2 ⊢ 𝐴 ⊆ 𝐴 | |
2 | 1 | a1i 9 | 1 ⊢ (𝜑 → 𝐴 ⊆ 𝐴) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ⊆ wss 3041 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-in 3047 df-ss 3054 |
This theorem is referenced by: isum 11122 fsum3ser 11134 fsumcl 11137 ennnfoneleminc 11851 restopn2 12279 negcncf 12684 mulcncf 12687 dvidlemap 12756 dvaddxxbr 12761 dvmulxxbr 12762 dvcoapbr 12767 dvcjbr 12768 dvexp 12771 dvrecap 12773 dvmptcmulcn 12779 dvmptnegcn 12780 dvmptsubcn 12781 dveflem 12782 dvef 12783 |
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