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Mirrors > Home > NFE Home > Th. List > pm4.71 | Unicode version |
Description: Implication in terms of biconditional and conjunction. Theorem *4.71 of [WhiteheadRussell] p. 120. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 2-Dec-2012.) |
Ref | Expression |
---|---|
pm4.71 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 443 | . . 3 | |
2 | 1 | biantru 491 | . 2 |
3 | anclb 530 | . 2 | |
4 | dfbi2 609 | . 2 | |
5 | 2, 3, 4 | 3bitr4i 268 | 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: pm4.71r 612 pm4.71i 613 pm4.71d 615 bigolden 901 pm5.75 903 exintrbi 1613 rabid2 2788 dfss2 3262 disj3 3595 dmopab3 4917 resopab2 5001 resoprab2 5582 |
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