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Mirrors > Home > ILE Home > Th. List > 3anim123d | Unicode version |
Description: Deduction joining 3 implications to form implication of conjunctions. (Contributed by NM, 24-Feb-2005.) |
Ref | Expression |
---|---|
3anim123d.1 | |
3anim123d.2 | |
3anim123d.3 |
Ref | Expression |
---|---|
3anim123d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3anim123d.1 | . . . 4 | |
2 | 3anim123d.2 | . . . 4 | |
3 | 1, 2 | anim12d 318 | . . 3 |
4 | 3anim123d.3 | . . 3 | |
5 | 3, 4 | anim12d 318 | . 2 |
6 | df-3an 887 | . 2 | |
7 | df-3an 887 | . 2 | |
8 | 5, 6, 7 | 3imtr4g 194 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 w3a 885 |
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 df-3an 887 |
This theorem is referenced by: hb3and 1379 pofun 4049 soss 4051 wessep 4302 isopolem 5461 isosolem 5463 issmo2 5904 smores 5907 |
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