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Mirrors > Home > MPE Home > Th. List > pm4.72 | Structured version Visualization version 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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | olc 399 | . . 3 | |
2 | pm2.621 424 | . . 3 | |
3 | 1, 2 | impbid2 216 | . 2 |
4 | orc 400 | . . 3 | |
5 | biimpr 210 | . . 3 | |
6 | 4, 5 | syl5 34 | . 2 |
7 | 3, 6 | impbii 199 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wo 383 |
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 197 df-or 385 |
This theorem is referenced by: bigolden 976 cadan 1548 ssequn1 3783 ssunsn2 4359 vtxd0nedgb 26384 bj-consensusALT 32563 elpaddn0 35086 |
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