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Mirrors > Home > MPE Home > Th. List > jcab | Structured version 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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 457 |
. . . 4
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2 | 1 | imim2i 14 |
. . 3
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3 | simpr 461 |
. . . 4
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4 | 3 | imim2i 14 |
. . 3
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5 | 2, 4 | jca 532 |
. 2
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6 | pm3.43 857 |
. 2
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7 | 5, 6 | impbii 188 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() |
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 185 df-an 371 |
This theorem is referenced by: ordi 859 pm4.76 861 pm5.44 902 2mo2 2367 2eu4OLD 2377 ssconb 3592 ssin 3675 tfr3 6963 isprm2 13884 lgsquad2lem2 22826 ostthlem2 23005 2reu4a 30156 pclclN 33854 |
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