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Mirrors > Home > ILE Home > Th. List > pm4.78i | Unicode version |
Description: Implication distributes over disjunction. One direction of Theorem *4.78 of [WhiteheadRussell] p. 121. The converse holds in classical logic. (Contributed by Jim Kingdon, 15-Jan-2018.) |
Ref | Expression |
---|---|
pm4.78i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | orc 712 |
. . 3
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2 | 1 | imim2i 12 |
. 2
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3 | olc 711 |
. . 3
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4 | 3 | imim2i 12 |
. 2
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5 | 2, 4 | jaoi 716 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: (None) |
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