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Mirrors > Home > MPE Home > Th. List > ex-ss | Structured version Visualization version GIF version |
Description: Example for df-ss 3952. Example by David A. Wheeler. (Contributed by Mario Carneiro, 6-May-2015.) |
Ref | Expression |
---|---|
ex-ss | ⊢ {1, 2} ⊆ {1, 2, 3} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssun1 4148 | . 2 ⊢ {1, 2} ⊆ ({1, 2} ∪ {3}) | |
2 | df-tp 4572 | . 2 ⊢ {1, 2, 3} = ({1, 2} ∪ {3}) | |
3 | 1, 2 | sseqtrri 4004 | 1 ⊢ {1, 2} ⊆ {1, 2, 3} |
Colors of variables: wff setvar class |
Syntax hints: ∪ cun 3934 ⊆ wss 3936 {csn 4567 {cpr 4569 {ctp 4571 1c1 10538 2c2 11693 3c3 11694 |
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 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-v 3496 df-un 3941 df-in 3943 df-ss 3952 df-tp 4572 |
This theorem is referenced by: ex-pss 28207 |
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