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Mirrors > Home > MPE Home > Th. List > ex-ss | Structured version Visualization version GIF version |
Description: Example for df-ss 3950. 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 4146 | . 2 ⊢ {1, 2} ⊆ ({1, 2} ∪ {3}) | |
2 | df-tp 4564 | . 2 ⊢ {1, 2, 3} = ({1, 2} ∪ {3}) | |
3 | 1, 2 | sseqtrri 4002 | 1 ⊢ {1, 2} ⊆ {1, 2, 3} |
Colors of variables: wff setvar class |
Syntax hints: ∪ cun 3932 ⊆ wss 3934 {csn 4559 {cpr 4561 {ctp 4563 1c1 10530 2c2 11684 3c3 11685 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1905 ax-6 1964 ax-7 2009 ax-8 2110 ax-9 2118 ax-10 2139 ax-11 2154 ax-12 2170 ax-ext 2791 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1534 df-ex 1775 df-nf 1779 df-sb 2064 df-clab 2798 df-cleq 2812 df-clel 2891 df-nfc 2961 df-v 3495 df-un 3939 df-in 3941 df-ss 3950 df-tp 4564 |
This theorem is referenced by: ex-pss 28199 |
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