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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 4715 | . 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵, 𝐴} | |
2 | tpidm12 4721 | . 2 ⊢ {𝐴, 𝐴, 𝐵} = {𝐴, 𝐵} | |
3 | 1, 2 | eqtr3i 2767 | 1 ⊢ {𝐴, 𝐵, 𝐴} = {𝐴, 𝐵} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 {cpr 4593 {ctp 4595 |
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-3or 1089 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-sn 4592 df-pr 4594 df-tp 4596 |
This theorem is referenced by: fntpb 7164 hashtpg 14391 |
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