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Mirrors > Home > MPE Home > Th. List > txtop | Unicode version |
Description: The product of two topologies is a topology. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
txtop |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2412 |
. . 3
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2 | 1 | txval 17557 |
. 2
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3 | topbas 17000 |
. . . 4
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4 | topbas 17000 |
. . . 4
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5 | 1 | txbas 17560 |
. . . 4
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6 | 3, 4, 5 | syl2an 464 |
. . 3
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7 | tgcl 16997 |
. . 3
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8 | 6, 7 | syl 16 |
. 2
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9 | 2, 8 | eqeltrd 2486 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: txtopi 17583 txtopon 17584 txcld 17596 neitx 17600 txlly 17629 txnlly 17630 txcmplem1 17634 txcmp 17636 hausdiag 17638 txhaus 17640 tx1stc 17643 txkgen 17645 xkococn 17653 xkoinjcn 17680 txcon 17682 imasnopn 17683 imasncls 17685 utop2nei 18241 utop3cls 18242 txpcon 24880 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-13 1723 ax-14 1725 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2393 ax-sep 4298 ax-nul 4306 ax-pow 4345 ax-pr 4371 ax-un 4668 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3an 938 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-eu 2266 df-mo 2267 df-clab 2399 df-cleq 2405 df-clel 2408 df-nfc 2537 df-ne 2577 df-ral 2679 df-rex 2680 df-rab 2683 df-v 2926 df-sbc 3130 df-csb 3220 df-dif 3291 df-un 3293 df-in 3295 df-ss 3302 df-nul 3597 df-if 3708 df-pw 3769 df-sn 3788 df-pr 3789 df-op 3791 df-uni 3984 df-iun 4063 df-br 4181 df-opab 4235 df-mpt 4236 df-id 4466 df-xp 4851 df-rel 4852 df-cnv 4853 df-co 4854 df-dm 4855 df-rn 4856 df-res 4857 df-ima 4858 df-iota 5385 df-fun 5423 df-fn 5424 df-f 5425 df-fv 5429 df-ov 6051 df-oprab 6052 df-mpt2 6053 df-1st 6316 df-2nd 6317 df-topgen 13630 df-top 16926 df-bases 16928 df-tx 17555 |
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