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Mirrors > Home > MPE Home > Th. List > tpnzd | Structured version Visualization version Unicode version |
Description: A triplet containing a set is not empty. (Contributed by Thierry Arnoux, 8-Apr-2019.) |
Ref | Expression |
---|---|
tpnzd.1 |
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Ref | Expression |
---|---|
tpnzd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tpnzd.1 |
. 2
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2 | tpid3g 4090 |
. . 3
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3 | tprot 4070 |
. . 3
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4 | 2, 3 | syl6eleqr 2542 |
. 2
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5 | ne0i 3739 |
. 2
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6 | 1, 4, 5 | 3syl 18 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 ax-ext 2433 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 987 df-tru 1449 df-ex 1666 df-nf 1670 df-sb 1800 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2583 df-ne 2626 df-v 3049 df-dif 3409 df-un 3411 df-nul 3734 df-sn 3971 df-pr 3973 df-tp 3975 |
This theorem is referenced by: raltpd 4098 fr3nr 6611 etransclem48OLD 38157 etransclem48 38158 |
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