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Mirrors > Home > ILE Home > Th. List > mtord | Unicode version |
Description: A modus tollens deduction involving disjunction. (Contributed by Jeff Hankins, 15-Jul-2009.) (Revised by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
mtord.1 | |
mtord.2 | |
mtord.3 |
Ref | Expression |
---|---|
mtord |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mtord.3 | . . 3 | |
2 | mtord.1 | . . . . 5 | |
3 | 2 | pm2.21d 549 | . . . 4 |
4 | mtord.2 | . . . . 5 | |
5 | 4 | pm2.21d 549 | . . . 4 |
6 | 3, 5 | jaod 637 | . . 3 |
7 | 1, 6 | syld 40 | . 2 |
8 | 7 | pm2.01d 548 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wo 629 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: swoer 6134 |
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