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Mirrors > Home > MPE Home > Th. List > prcom | Structured version Visualization version GIF version |
Description: Commutative law for unordered pairs. (Contributed by NM, 15-Jul-1993.) |
Ref | Expression |
---|---|
prcom | ⊢ {𝐴, 𝐵} = {𝐵, 𝐴} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uncom 4067 | . 2 ⊢ ({𝐴} ∪ {𝐵}) = ({𝐵} ∪ {𝐴}) | |
2 | df-pr 4544 | . 2 ⊢ {𝐴, 𝐵} = ({𝐴} ∪ {𝐵}) | |
3 | df-pr 4544 | . 2 ⊢ {𝐵, 𝐴} = ({𝐵} ∪ {𝐴}) | |
4 | 1, 2, 3 | 3eqtr4i 2775 | 1 ⊢ {𝐴, 𝐵} = {𝐵, 𝐴} |
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