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Mirrors > Home > NFE Home > Th. List > prth | Unicode version |
Description: Conjoin antecedents and consequents of two premises. This is the closed theorem form of anim12d 546. Theorem *3.47 of [WhiteheadRussell] p. 113. It was proved by Leibniz, and it evidently pleased him enough to call it praeclarum theorema (splendid theorem). (Contributed by NM, 12-Aug-1993.) (Proof shortened by Wolf Lammen, 7-Apr-2013.) |
Ref | Expression |
---|---|
prth |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 443 | . 2 | |
2 | simpr 447 | . 2 | |
3 | 1, 2 | anim12d 546 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 177 df-an 360 |
This theorem is referenced by: mo 2226 2mo 2282 euind 3023 reuind 3039 reuss2 3535 opelopabt 4699 |
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