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Mirrors > Home > MPE Home > Th. List > tpidm13 | Structured version Visualization version GIF version |
Description: Unordered triple {𝐴, 𝐵, 𝐴} is just an overlong way to write {𝐴, 𝐵}. (Contributed by David A. Wheeler, 10-May-2015.) |
Ref | Expression |
---|---|
tpidm13 | ⊢ {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tprot 4687 | . 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵, 𝐴} | |
2 | tpidm12 4693 | . 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵} | |
3 | 1, 2 | eqtr3i 2848 | 1 ⊢ {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 {cpr 4571 {ctp 4573 |
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-3or 1084 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-v 3498 df-un 3943 df-sn 4570 df-pr 4572 df-tp 4574 |
This theorem is referenced by: fntpb 6974 hashtpg 13846 |
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