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Mirrors > Home > MPE Home > Th. List > ax13 | Structured version Visualization version Unicode version |
Description: Derive ax-13 2091 from ax13v 2092 via axc9 2140. This shows that the weakening in ax13v 2092 is still sufficient for a complete system. (Contributed by NM, 21-Dec-2015.) (Proof shortened by Wolf Lammen, 31-Jan-2018.) |
Ref | Expression |
---|---|
ax13 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sp 1937 |
. . . 4
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2 | 1 | con3i 141 |
. . 3
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3 | sp 1937 |
. . . 4
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4 | 3 | con3i 141 |
. . 3
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5 | axc9 2140 |
. . 3
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6 | 2, 4, 5 | syl2im 39 |
. 2
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7 | ax13b 1874 |
. 2
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8 | 6, 7 | mpbir 213 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-12 1933 ax-13 2091 |
This theorem depends on definitions: df-bi 189 df-an 373 df-ex 1664 df-nf 1668 |
This theorem is referenced by: equvini 2179 sbequi 2204 |
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