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Mirrors > Home > NFE Home > Th. List > mpancom | Unicode version |
Description: An inference based on modus ponens with commutation of antecedents. (Contributed by NM, 28-Oct-2003.) (Proof shortened by Wolf Lammen, 7-Apr-2013.) |
Ref | Expression |
---|---|
mpancom.1 | |
mpancom.2 |
Ref | Expression |
---|---|
mpancom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpancom.1 | . 2 | |
2 | id 19 | . 2 | |
3 | mpancom.2 | . 2 | |
4 | 1, 2, 3 | syl2anc 642 | 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: mpan 651 spesbc 3127 nnc3n3p1 6278 nnc3n3p2 6279 nnc3p1n3p2 6280 |
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