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Mirrors > Home > ILE Home > Th. List > unex | Unicode version |
Description: The union of two sets is a set. Corollary 5.8 of [TakeutiZaring] p. 16. (Contributed by NM, 1-Jul-1994.) |
Ref | Expression |
---|---|
unex.1 |
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unex.2 |
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Ref | Expression |
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unex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unex.1 |
. . 3
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2 | unex.2 |
. . 3
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3 | 1, 2 | unipr 3585 |
. 2
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4 | prexgOLD 3937 |
. . . 4
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5 | 1, 2, 4 | mp2an 402 |
. . 3
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6 | 5 | uniex 4140 |
. 2
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7 | 3, 6 | eqeltrri 2108 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-13 1401 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-sep 3866 ax-pr 3935 ax-un 4136 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-rex 2306 df-v 2553 df-un 2916 df-sn 3373 df-pr 3374 df-uni 3572 |
This theorem is referenced by: unexb 4143 rdg0 5914 unen 6229 nn0ex 7963 xrex 8526 |
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