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Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-sb8et | Structured version Visualization version Unicode version |
Description: Substitution of variable in universal quantifier. Closed form of sb8e 2264. (Contributed by Wolf Lammen, 27-Jul-2019.) |
Ref | Expression |
---|---|
wl-sb8et |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wl-nfnbi 31903 |
. . . . 5
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2 | 1 | albii 1701 |
. . . 4
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3 | wl-sb8t 31924 |
. . . 4
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4 | 2, 3 | sylbi 200 |
. . 3
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5 | alnex 1675 |
. . 3
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6 | sbn 2230 |
. . . . 5
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7 | 6 | albii 1701 |
. . . 4
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8 | alnex 1675 |
. . . 4
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9 | 7, 8 | bitri 257 |
. . 3
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10 | 4, 5, 9 | 3bitr3g 295 |
. 2
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11 | 10 | con4bid 299 |
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 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-ex 1674 df-nf 1678 df-sb 1808 |
This theorem is referenced by: wl-mo3t 31949 wl-sb8mot 31951 |
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