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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 4640 | . 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵, 𝐴} | |
2 | tpidm12 4646 | . 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵} | |
3 | 1, 2 | eqtr3i 2763 | 1 ⊢ {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 {cpr 4518 {ctp 4520 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1917 ax-6 1975 ax-7 2020 ax-8 2116 ax-9 2124 ax-ext 2710 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 847 df-3or 1089 df-tru 1545 df-ex 1787 df-sb 2075 df-clab 2717 df-cleq 2730 df-clel 2811 df-v 3400 df-un 3848 df-sn 4517 df-pr 4519 df-tp 4521 |
This theorem is referenced by: fntpb 6982 hashtpg 13937 |
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