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Mirrors > Home > ILE Home > Th. List > sylnibr | Unicode version |
Description: A mixed syllogism inference from an implication and a biconditional. Useful for substituting an consequent with a definition. (Contributed by Wolf Lammen, 16-Dec-2013.) |
Ref | Expression |
---|---|
sylnibr.1 | |
sylnibr.2 |
Ref | Expression |
---|---|
sylnibr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylnibr.1 | . 2 | |
2 | sylnibr.2 | . . 3 | |
3 | 2 | bicomi 131 | . 2 |
4 | 1, 3 | sylnib 666 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: rexnalim 2453 nssr 3197 difdif 3242 unssin 3356 inssun 3357 undif3ss 3378 ssdif0im 3468 dcun 3514 prneimg 3748 iundif2ss 3925 nssssr 4194 pofun 4284 frirrg 4322 regexmidlem1 4504 dcdifsnid 6463 unfidisj 6878 fidcenumlemrks 6909 difinfsn 7056 pw1nel3 7178 addnqprlemfl 7491 addnqprlemfu 7492 mulnqprlemfl 7507 mulnqprlemfu 7508 cauappcvgprlemladdru 7588 caucvgprprlemaddq 7640 fzpreddisj 9996 fprodntrivap 11511 pw2dvdslemn 12076 ivthinclemdisj 13165 pwtrufal 13718 pw1nct 13724 nninfsellemsuc 13733 |
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