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Mirrors > Home > ILE Home > Th. List > syl3an3 | Unicode version |
Description: A syllogism inference. (Contributed by NM, 22-Aug-1995.) |
Ref | Expression |
---|---|
syl3an3.1 | |
syl3an3.2 |
Ref | Expression |
---|---|
syl3an3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl3an3.1 | . . 3 | |
2 | syl3an3.2 | . . . 4 | |
3 | 2 | 3exp 1137 | . . 3 |
4 | 1, 3 | syl7 68 | . 2 |
5 | 4 | 3imp 1132 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 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: syl3an3b 1207 syl3an3br 1210 vtoclgft 2649 ovmpt2x 5649 ovmpt2ga 5650 nnanq0 6648 apreim 7703 divassap 7778 ltmul2 7934 elfzo 9159 subcn2 10150 mulcn2 10151 ndvdsp1 10332 gcddiv 10408 lcmneg 10456 |
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