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Mirrors > Home > NFE Home > Th. List > exsb | Unicode version |
Description: An equivalent expression for existence. (Contributed by NM, 2-Feb-2005.) |
Ref | Expression |
---|---|
exsb |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1619 |
. 2
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2 | nfa1 1788 |
. 2
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3 | ax11v 2096 |
. . 3
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4 | sp 1747 |
. . . 4
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5 | 4 | com12 27 |
. . 3
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6 | 3, 5 | impbid 183 |
. 2
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7 | 1, 2, 6 | cbvex 1985 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 |
This theorem is referenced by: 2exsb 2132 |
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