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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.67-2 634 | . . . 4 | |
2 | 1 | ibd 167 | . . 3 |
3 | olc 632 | . . . . 5 | |
4 | 3 | imim1i 54 | . . . 4 |
5 | ibibr 235 | . . . 4 | |
6 | 4, 5 | sylibr 137 | . . 3 |
7 | 2, 6 | impbid 120 | . 2 |
8 | ax-1 5 | . 2 | |
9 | 7, 8 | impbii 117 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wo 629 |
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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