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| Mirrors > Home > ILE Home > Th. List > mtbi | Unicode version | ||
| Description: An inference from a biconditional, related to modus tollens. (Contributed by NM, 15-Nov-1994.) (Proof shortened by Wolf Lammen, 25-Oct-2012.) |
| Ref | Expression |
|---|---|
| mtbi.1 |
|
| mtbi.2 |
|
| Ref | Expression |
|---|---|
| mtbi |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mtbi.1 |
. 2
| |
| 2 | mtbi.2 |
. . 3
| |
| 3 | 2 | biimpri 133 |
. 2
|
| 4 | 1, 3 | mto 663 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 |
| This theorem depends on definitions: df-bi 117 |
| This theorem is referenced by: mtbir 672 vnex 4164 onsucelsucexmid 4566 dtruex 4595 dmsn0 5137 php5 6919 exmidonfinlem 7260 ndvdsi 12098 nprmi 12292 dec2dvds 12580 dec5dvds2 12582 unennn 12614 bj-vprc 15542 bj-vnex 15544 trirec0xor 15689 |
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