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Mirrors > Home > MPE Home > Th. List > 3orim123d | Structured version Visualization version 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 883 | . . 3 |
4 | 3anim123d.3 | . . 3 | |
5 | 3, 4 | orim12d 883 | . 2 |
6 | df-3or 1038 | . 2 | |
7 | df-3or 1038 | . 2 | |
8 | 5, 6, 7 | 3imtr4g 285 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wo 383 w3o 1036 |
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 df-an 386 df-3or 1038 |
This theorem is referenced by: fr3nr 6979 soxp 7290 zorn2lem6 9323 fpwwe2lem12 9463 fpwwe2lem13 9464 colinearalglem4 25789 sltres 31815 colinearxfr 32182 fin2so 33396 frege133d 38057 el1fzopredsuc 41335 fmtno4prmfac 41484 |
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