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Mirrors > Home > ILE Home > Th. List > syl3an9b | Unicode version |
Description: Nested syllogism inference conjoining 3 dissimilar antecedents. (Contributed by NM, 1-May-1995.) |
Ref | Expression |
---|---|
syl3an9b.1 | |
syl3an9b.2 | |
syl3an9b.3 |
Ref | Expression |
---|---|
syl3an9b |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl3an9b.1 | . . . 4 | |
2 | syl3an9b.2 | . . . 4 | |
3 | 1, 2 | sylan9bb 449 | . . 3 |
4 | syl3an9b.3 | . . 3 | |
5 | 3, 4 | sylan9bb 449 | . 2 |
6 | 5 | 3impa 1133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 w3a 919 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-3an 921 |
This theorem is referenced by: eloprabg 5612 |
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