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Mirrors > Home > ILE Home > Th. List > mtbii | Unicode version |
Description: An inference from a biconditional, similar to modus tollens. (Contributed by NM, 27-Nov-1995.) |
Ref | Expression |
---|---|
mtbii.min | |
mtbii.maj |
Ref | Expression |
---|---|
mtbii |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mtbii.min | . 2 | |
2 | mtbii.maj | . . 3 | |
3 | 2 | biimprd 157 | . 2 |
4 | 1, 3 | mtoi 659 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 609 ax-in2 610 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: onsucelsucexmid 4512 nntri2 6470 nntri3 6473 nndceq 6475 inffiexmid 6880 genpdisj 7472 ltposr 7712 hashennn 10701 fsumsplit 11357 sumsplitdc 11382 fprodm1 11548 m1dvdsndvds 12189 |
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