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Mirrors > Home > ILE Home > Th. List > sban | Unicode version |
Description: Conjunction inside and outside of a substitution are equivalent. (Contributed by NM, 5-Aug-1993.) (Proof rewritten by Jim Kingdon, 3-Feb-2018.) |
Ref | Expression |
---|---|
sban |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbanv 1889 |
. . . 4
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2 | 1 | sbbii 1765 |
. . 3
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3 | sbanv 1889 |
. . 3
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4 | 2, 3 | bitri 184 |
. 2
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5 | ax-17 1526 |
. . 3
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6 | 5 | sbco2vh 1945 |
. 2
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7 | ax-17 1526 |
. . . 4
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8 | 7 | sbco2vh 1945 |
. . 3
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9 | ax-17 1526 |
. . . 4
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10 | 9 | sbco2vh 1945 |
. . 3
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11 | 8, 10 | anbi12i 460 |
. 2
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12 | 4, 6, 11 | 3bitr3i 210 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 |
This theorem is referenced by: sb3an 1958 sbbi 1959 sbmo 2085 moanim 2100 sbabel 2346 nfrexdya 2513 cbvreu 2701 rmo3f 2934 sbcan 3005 sbcang 3006 rmo3 3054 inab 3403 difab 3404 exss 4223 inopab 4754 bdcriota 14257 |
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