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Mirrors > Home > NFE 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 443 | . . . 4 | |
2 | 1 | imim2i 13 | . . 3 |
3 | simpr 447 | . . . 4 | |
4 | 3 | imim2i 13 | . . 3 |
5 | 2, 4 | jca 518 | . 2 |
6 | pm3.43 832 | . 2 | |
7 | 5, 6 | impbii 180 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 |
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 177 df-an 360 |
This theorem is referenced by: ordi 834 pm4.76 836 pm5.44 877 2eu4 2287 ssconb 3399 ssin 3477 |
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