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Mirrors > Home > ILE Home > Th. List > jcab | Unicode version |
Description: Distributive law for implication over conjunction. Compare Theorem *4.76 of [WhiteheadRussell] p. 121. (Contributed by NM, 3-Apr-1994.) (Proof shortened by Wolf Lammen, 27-Nov-2013.) |
Ref | Expression |
---|---|
jcab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 108 | . . . 4 | |
2 | 1 | imim2i 12 | . . 3 |
3 | simpr 109 | . . . 4 | |
4 | 3 | imim2i 12 | . . 3 |
5 | 2, 4 | jca 304 | . 2 |
6 | pm3.43 592 | . 2 | |
7 | 5, 6 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 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 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: pm4.76 594 pm5.44 911 2eu4 2099 ssconb 3241 ssin 3330 raaan 3501 tfri3 6316 omniwomnimkv 7112 isprm2 12009 |
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