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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 1103 | . . 3 |
4 | 1, 3 | syl7 63 | . 2 |
5 | 4 | 3imp 1098 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 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: syl3an3b 1173 syl3an3br 1176 vtoclgft 2604 ovmpt2x 5629 ovmpt2ga 5630 nnanq0 6556 apreim 7594 divassap 7669 ltmul2 7822 elfzo 9006 subcn2 9832 mulcn2 9833 |
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