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Mirrors > Home > ILE Home > Th. List > Mathboxes > alsi2d | Unicode version |
Description: Deduction rule: Given "all some" applied to a top-level inference, you can extract the "exists" part. (Contributed by David A. Wheeler, 20-Oct-2018.) |
Ref | Expression |
---|---|
alsi2d.1 | ! |
Ref | Expression |
---|---|
alsi2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alsi2d.1 | . . 3 ! | |
2 | df-alsi 13815 | . . 3 ! | |
3 | 1, 2 | sylib 121 | . 2 |
4 | 3 | simprd 113 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1340 wex 1479 !walsi 13813 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 |
This theorem depends on definitions: df-bi 116 df-alsi 13815 |
This theorem is referenced by: (None) |
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