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On some weakening of intuitionistic logic
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part IV, Tome 20 (1971), pp. 208-219 Cet article a éte moissonné depuis la source Math-Net.Ru

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There is considered calculus $K$ obtained from the intuitionistic propositional calculus by means of replacing the axiom $(p\supset q)\supset((p\supset r)\supset(p\supset q\&r))$ by the rule: $F\supset G$, $F\supset H\vdash F\supset(G\&H)$. 
@article{ZNSL_1971_20_a19,
     author = {Yu. N. Tolstova},
     title = {On some weakening of intuitionistic logic},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {208--219},
     year = {1971},
     volume = {20},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1971_20_a19/}
}
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Yu. N. Tolstova. On some weakening of intuitionistic logic. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part IV, Tome 20 (1971), pp. 208-219. http://geodesic.mathdoc.fr/item/ZNSL_1971_20_a19/