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Mirrors > Home > MPE Home > Th. List > sbal | Structured version Visualization version Unicode version |
Description: Move universal quantifier in and out of substitution. (Contributed by NM, 16-May-1993.) (Proof shortened by Wolf Lammen, 29-Sep-2018.) |
Ref | Expression |
---|---|
sbal |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfae 2165 |
. . . 4
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2 | axc16gb 2044 |
. . . 4
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3 | 1, 2 | sbbid 2252 |
. . 3
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4 | axc16gb 2044 |
. . 3
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5 | 3, 4 | bitr3d 263 |
. 2
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6 | sbal1 2309 |
. 2
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7 | 5, 6 | pm2.61i 169 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-ex 1672 df-nf 1676 df-sb 1806 |
This theorem is referenced by: sbex 2312 sbalv 2313 sbcal 3305 ax11-pm2 31504 bj-sbnf 31509 sbcalgOLD 36973 |
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