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Mirrors > Home > ILE Home > Th. List > 3jaao | Unicode version |
Description: Inference conjoining and disjoining the antecedents of three implications. (Contributed by Jeff Hankins, 15-Aug-2009.) (Proof shortened by Andrew Salmon, 13-May-2011.) |
Ref | Expression |
---|---|
3jaao.1 | |
3jaao.2 | |
3jaao.3 |
Ref | Expression |
---|---|
3jaao |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3jaao.1 | . . 3 | |
2 | 1 | 3ad2ant1 1003 | . 2 |
3 | 3jaao.2 | . . 3 | |
4 | 3 | 3ad2ant2 1004 | . 2 |
5 | 3jaao.3 | . . 3 | |
6 | 5 | 3ad2ant3 1005 | . 2 |
7 | 2, 4, 6 | 3jaod 1286 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 w3o 962 w3a 963 |
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 699 |
This theorem depends on definitions: df-bi 116 df-3or 964 df-3an 965 |
This theorem is referenced by: (None) |
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