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Mirrors > Home > ILE Home > Th. List > syl8 | Unicode version |
Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. (Contributed by NM, 1-Aug-1994.) (Proof shortened by Wolf Lammen, 3-Aug-2012.) |
Ref | Expression |
---|---|
syl8.1 | |
syl8.2 |
Ref | Expression |
---|---|
syl8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | syl8.1 | . 2 | |
2 | syl8.2 | . . 3 | |
3 | 2 | a1i 9 | . 2 |
4 | 1, 3 | syl6d 69 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 |
This theorem is referenced by: com45 88 syl8ib 164 imp5a 350 con4biddc 787 3exp 1137 suctr 4176 ssorduni 4231 nneneq 6343 qreccl 8727 bj-inf2vnlem2 10766 |
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