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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 5802 | . 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 3929 ran crn 5549 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1969 ax-7 2014 ax-8 2115 ax-9 2123 ax-10 2144 ax-11 2160 ax-12 2176 ax-ext 2792 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1084 df-tru 1539 df-ex 1780 df-nf 1784 df-sb 2069 df-clab 2799 df-cleq 2813 df-clel 2892 df-nfc 2962 df-rab 3146 df-v 3493 df-dif 3932 df-un 3934 df-in 3936 df-ss 3945 df-nul 4285 df-if 4461 df-sn 4561 df-pr 4563 df-op 4567 df-br 5060 df-opab 5122 df-cnv 5556 df-dm 5558 df-rn 5559 |
This theorem is referenced by: ssrnres 6028 fssres 6537 smores 7982 brdom4 9945 smobeth 10001 nqerf 10345 catcoppccl 17363 lern 17830 gsumzres 19024 gsumzaddlem 19036 gsumzadd 19037 dprdfadd 19137 txkgen 22255 dvlog 25232 perpln2 26495 pfxrn2 30616 fixssrn 33389 cnvrcl0 40059 rnresss 41513 |
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