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Mirrors > Home > MPE Home > Th. List > orcs | Structured version Visualization version Unicode version |
Description: Deduction eliminating disjunct. Notational convention: We sometimes suffix with "s" the label of an inference that manipulates an antecedent, leaving the consequent unchanged. The "s" means that the inference eliminates the need for a syllogism (syl 17) -type inference in a proof. (Contributed by NM, 21-Jun-1994.) |
Ref | Expression |
---|---|
orcs.1 |
Ref | Expression |
---|---|
orcs |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 400 | . 2 | |
2 | orcs.1 | . 2 | |
3 | 1, 2 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wo 383 |
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 |
This theorem is referenced by: olcs 410 ifor 4135 tppreqb 4336 frxp 7287 mndifsplit 20442 maducoeval2 20446 leibpilem2 24668 leibpi 24669 3o1cs 29309 3o2cs 29310 poimirlem31 33440 tsan2 33949 frege114d 38050 ntrneiel2 38384 nnfoctbdjlem 40672 |
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