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Mirrors > Home > ILE Home > Th. List > addcomnqg | Unicode version |
Description: Addition of positive fractions is commutative. (Contributed by Jim Kingdon, 15-Sep-2019.) |
Ref | Expression |
---|---|
addcomnqg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nqqs 6968 |
. 2
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2 | addpipqqs 6990 |
. 2
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3 | addpipqqs 6990 |
. 2
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4 | mulcompig 6951 |
. . . . 5
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5 | mulcompig 6951 |
. . . . 5
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6 | 4, 5 | oveqan12d 5685 |
. . . 4
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7 | 6 | an42s 557 |
. . 3
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8 | mulclpi 6948 |
. . . . . 6
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9 | 8 | ancoms 265 |
. . . . 5
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10 | 9 | ad2ant2rl 496 |
. . . 4
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11 | mulclpi 6948 |
. . . . . 6
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12 | 11 | ancoms 265 |
. . . . 5
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13 | 12 | ad2ant2lr 495 |
. . . 4
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14 | addcompig 6949 |
. . . 4
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15 | 10, 13, 14 | syl2anc 404 |
. . 3
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16 | 7, 15 | eqtrd 2121 |
. 2
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17 | mulcompig 6951 |
. . 3
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18 | 17 | ad2ant2l 493 |
. 2
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19 | 1, 2, 3, 16, 18 | ecovicom 6414 |
1
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