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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 4685 | . 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵, 𝐴} | |
2 | tpidm12 4691 | . 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵} | |
3 | 1, 2 | eqtr3i 2768 | 1 ⊢ {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1539 {cpr 4563 {ctp 4565 |
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 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2709 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-3or 1087 df-tru 1542 df-ex 1783 df-sb 2068 df-clab 2716 df-cleq 2730 df-clel 2816 df-v 3434 df-un 3892 df-sn 4562 df-pr 4564 df-tp 4566 |
This theorem is referenced by: fntpb 7085 hashtpg 14199 |
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