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Mirrors > Home > MPE Home > Th. List > rnssi | Structured version Visualization version GIF version |
Description: Subclass inference for range. (Contributed by Peter Mazsa, 24-Sep-2022.) |
Ref | Expression |
---|---|
rnssi.1 | ⊢ 𝐴 ⊆ 𝐵 |
Ref | Expression |
---|---|
rnssi | ⊢ ran 𝐴 ⊆ ran 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rnssi.1 | . 2 ⊢ 𝐴 ⊆ 𝐵 | |
2 | rnss 5941 | . 2 ⊢ (𝐴 ⊆ 𝐵 → ran 𝐴 ⊆ ran 𝐵) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ran 𝐴 ⊆ ran 𝐵 |
Colors of variables: wff setvar class |
Syntax hints: ⊆ wss 3944 ran crn 5679 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2696 |
This theorem depends on definitions: df-bi 206 df-an 395 df-or 846 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 df-rab 3419 df-v 3463 df-dif 3947 df-un 3949 df-ss 3961 df-nul 4323 df-if 4531 df-sn 4631 df-pr 4633 df-op 4637 df-br 5150 df-opab 5212 df-cnv 5686 df-dm 5688 df-rn 5689 |
This theorem is referenced by: rnresss 6022 ssrnres 6184 fssres 6763 smores 8373 rnttrcl 9747 brdom4 10555 smobeth 10611 nqerf 10955 catcoppccl 18109 catcoppcclOLD 18110 lern 18586 gsumzres 19876 gsumzaddlem 19888 gsumzadd 19889 dprdfadd 19989 txkgen 23600 dvlog 26630 perpln2 28587 pfxrn2 32750 fixssrn 35634 cnvrcl0 43197 |
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