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Mirrors > Home > NFE Home > Th. List > pm2.43i | GIF version |
Description: Inference absorbing redundant antecedent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by O'Cat, 28-Nov-2008.) |
Ref | Expression |
---|---|
pm2.43i.1 | ⊢ (φ → (φ → ψ)) |
Ref | Expression |
---|---|
pm2.43i | ⊢ (φ → ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ (φ → φ) | |
2 | pm2.43i.1 | . 2 ⊢ (φ → (φ → ψ)) | |
3 | 1, 2 | mpd 14 | 1 ⊢ (φ → ψ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 |
This theorem is referenced by: sylc 56 pm2.18 102 impbid 183 ibi 232 anidms 626 tbw-bijust 1463 tbw-negdf 1464 equid 1676 equidOLD 1677 hbae 1953 aecom-o 2151 hbae-o 2153 hbequid 2160 equidqe 2173 equid1ALT 2176 ax10from10o 2177 ax11inda 2200 vtoclgaf 2919 vtocl2gaf 2921 vtocl3gaf 2923 elinti 3935 spfinsfincl 4539 copsexg 4607 |
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