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Mirrors > Home > MPE Home > Th. List > ex-ss | Structured version Visualization version GIF version |
Description: Example for df-ss 3932. 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 4137 | . 2 ⊢ {1, 2} ⊆ ({1, 2} ∪ {3}) | |
2 | df-tp 4596 | . 2 ⊢ {1, 2, 3} = ({1, 2} ∪ {3}) | |
3 | 1, 2 | sseqtrri 3986 | 1 ⊢ {1, 2} ⊆ {1, 2, 3} |
Colors of variables: wff setvar class |
Syntax hints: ∪ cun 3913 ⊆ wss 3915 {csn 4591 {cpr 4593 {ctp 4595 1c1 11059 2c2 12215 3c3 12216 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2708 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2715 df-cleq 2729 df-clel 2815 df-v 3450 df-un 3920 df-in 3922 df-ss 3932 df-tp 4596 |
This theorem is referenced by: ex-pss 29414 |
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