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Mirrors > Home > MPE Home > Th. List > rex0 | Structured version Visualization version Unicode version |
Description: Vacuous existential quantification is false. (Contributed by NM, 15-Oct-2003.) |
Ref | Expression |
---|---|
rex0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3746 |
. . 3
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2 | 1 | pm2.21i 136 |
. 2
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3 | 2 | nrex 2853 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ral 2753 df-rex 2754 df-v 3058 df-dif 3418 df-nul 3743 |
This theorem is referenced by: 0iun 4348 sup0riota 8004 cfeq0 8711 cfsuc 8712 hashge2el2difr 12670 cshws0 15120 meet0 16431 join0 16432 dya2iocuni 29153 eulerpartlemgh 29259 pmapglb2xN 33381 elpadd0 33418 |
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