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Mirrors > Home > ILE Home > Th. List > pm5.74 | Unicode version |
Description: Distribution of implication over biconditional. Theorem *5.74 of [WhiteheadRussell] p. 126. (Contributed by NM, 1-Aug-1994.) (Proof shortened by Wolf Lammen, 11-Apr-2013.) |
Ref | Expression |
---|---|
pm5.74 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bi1 111 | . . . 4 | |
2 | 1 | imim3i 55 | . . 3 |
3 | bi2 121 | . . . 4 | |
4 | 3 | imim3i 55 | . . 3 |
5 | 2, 4 | impbid 120 | . 2 |
6 | bi1 111 | . . . 4 | |
7 | 6 | pm2.86d 93 | . . 3 |
8 | bi2 121 | . . . 4 | |
9 | 8 | pm2.86d 93 | . . 3 |
10 | 7, 9 | impbidd 118 | . 2 |
11 | 5, 10 | impbii 117 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: pm5.74i 169 pm5.74ri 170 pm5.74d 171 pm5.74rd 172 bibi2d 221 |
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