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Mirrors > Home > ILE Home > Th. List > pm4.72 | Unicode version |
Description: Implication in terms of biconditional and disjunction. Theorem *4.72 of [WhiteheadRussell] p. 121. (Contributed by NM, 30-Aug-1993.) (Proof shortened by Wolf Lammen, 30-Jan-2013.) |
Ref | Expression |
---|---|
pm4.72 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | olc 683 |
. . 3
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2 | pm2.621 719 |
. . 3
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3 | 1, 2 | impbid2 142 |
. 2
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4 | orc 684 |
. . 3
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5 | bi2 129 |
. . 3
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6 | 4, 5 | syl5 32 |
. 2
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7 | 3, 6 | impbii 125 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: bigolden 922 ssequn1 3212 |
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