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Mirrors > Home > ILE Home > Th. List > 3orim123d | Unicode version |
Description: Deduction joining 3 implications to form implication of disjunctions. (Contributed by NM, 4-Apr-1997.) |
Ref | Expression |
---|---|
3anim123d.1 | |
3anim123d.2 | |
3anim123d.3 |
Ref | Expression |
---|---|
3orim123d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anim123d.1 | . . . 4 | |
2 | 3anim123d.2 | . . . 4 | |
3 | 1, 2 | orim12d 781 | . . 3 |
4 | 3anim123d.3 | . . 3 | |
5 | 3, 4 | orim12d 781 | . 2 |
6 | df-3or 974 | . 2 | |
7 | df-3or 974 | . 2 | |
8 | 5, 6, 7 | 3imtr4g 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 703 w3o 972 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704 |
This theorem depends on definitions: df-bi 116 df-3or 974 |
This theorem is referenced by: ztri3or0 9247 |
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