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Mirrors > Home > ILE Home > Th. List > oibabs | Unicode version |
Description: Absorption of disjunction into equivalence. (Contributed by NM, 6-Aug-1995.) (Proof shortened by Wolf Lammen, 3-Nov-2013.) |
Ref | Expression |
---|---|
oibabs |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.67-2 634 |
. . . 4
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2 | 1 | ibd 167 |
. . 3
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3 | olc 632 |
. . . . 5
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4 | 3 | imim1i 54 |
. . . 4
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5 | ibibr 235 |
. . . 4
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6 | 4, 5 | sylibr 137 |
. . 3
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7 | 2, 6 | impbid 120 |
. 2
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8 | ax-1 5 |
. 2
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9 | 7, 8 | impbii 117 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: (None) |
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