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Mirrors > Home > MPE Home > Th. List > unfi | Structured version Visualization version Unicode version |
Description: The union of two finite sets is finite. Part of Corollary 6K of [Enderton] p. 144. (Contributed by NM, 16-Nov-2002.) |
Ref | Expression |
---|---|
unfi |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | diffi 7829 |
. 2
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2 | reeanv 2970 |
. . . 4
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3 | isfi 7619 |
. . . . 5
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4 | isfi 7619 |
. . . . 5
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5 | 3, 4 | anbi12i 708 |
. . . 4
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6 | 2, 5 | bitr4i 260 |
. . 3
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7 | nnacl 7338 |
. . . . 5
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8 | unfilem3 7863 |
. . . . . . 7
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9 | entr 7647 |
. . . . . . . 8
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10 | 9 | expcom 441 |
. . . . . . 7
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11 | 8, 10 | syl 17 |
. . . . . 6
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12 | disjdif 3851 |
. . . . . . . 8
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13 | disjdif 3851 |
. . . . . . . 8
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14 | unen 7678 |
. . . . . . . 8
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15 | 12, 13, 14 | mpanr12 696 |
. . . . . . 7
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16 | undif2 3855 |
. . . . . . . . 9
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17 | 16 | a1i 11 |
. . . . . . . 8
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18 | nnaword1 7356 |
. . . . . . . . 9
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19 | undif 3860 |
. . . . . . . . 9
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20 | 18, 19 | sylib 201 |
. . . . . . . 8
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21 | 17, 20 | breq12d 4429 |
. . . . . . 7
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22 | 15, 21 | syl5ib 227 |
. . . . . 6
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23 | 11, 22 | sylan2d 489 |
. . . . 5
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24 | breq2 4420 |
. . . . . . 7
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25 | 24 | rspcev 3162 |
. . . . . 6
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26 | isfi 7619 |
. . . . . 6
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27 | 25, 26 | sylibr 217 |
. . . . 5
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28 | 7, 23, 27 | syl6an 552 |
. . . 4
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29 | 28 | rexlimivv 2896 |
. . 3
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30 | 6, 29 | sylbir 218 |
. 2
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31 | 1, 30 | sylan2 481 |
1
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