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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 5811 | . 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 3938 ran crn 5558 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2795 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2802 df-cleq 2816 df-clel 2895 df-nfc 2965 df-rab 3149 df-v 3498 df-dif 3941 df-un 3943 df-in 3945 df-ss 3954 df-nul 4294 df-if 4470 df-sn 4570 df-pr 4572 df-op 4576 df-br 5069 df-opab 5131 df-cnv 5565 df-dm 5567 df-rn 5568 |
This theorem is referenced by: ssrnres 6037 fssres 6546 smores 7991 brdom4 9954 smobeth 10010 nqerf 10354 catcoppccl 17370 lern 17837 gsumzres 19031 gsumzaddlem 19043 gsumzadd 19044 dprdfadd 19144 txkgen 22262 dvlog 25236 perpln2 26499 pfxrn2 30618 fixssrn 33370 cnvrcl0 39992 rnresss 41446 |
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