Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-orel12 | Structured version Visualization version Unicode version |
Description: In a conjunctive normal form a pair of nodes like eliminates the need of a node . This theorem allows simplifications in that respect. (Contributed by Wolf Lammen, 20-Jun-2020.) |
Ref | Expression |
---|---|
wl-orel12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.1 433 | . 2 | |
2 | orel1 397 | . . . 4 | |
3 | orc 400 | . . . 4 | |
4 | 2, 3 | syl6com 37 | . . 3 |
5 | notnot 136 | . . . . 5 | |
6 | orel1 397 | . . . . 5 | |
7 | 5, 6 | syl 17 | . . . 4 |
8 | olc 399 | . . . 4 | |
9 | 7, 8 | syl6com 37 | . . 3 |
10 | 4, 9 | jaao 531 | . 2 |
11 | 1, 10 | mpi 20 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wo 383 wa 384 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 |
This theorem is referenced by: wl-cases2-dnf 33295 |
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