![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > sylnibr | Structured version Visualization version Unicode version |
Description: A mixed syllogism inference from an implication and a biconditional. Useful for substituting a consequent with a definition. (Contributed by Wolf Lammen, 16-Dec-2013.) |
Ref | Expression |
---|---|
sylnibr.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
sylnibr.2 |
![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
sylnibr |
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sylnibr.1 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | sylnibr.2 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 2 | bicomi 207 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() |
4 | 1, 3 | sylnib 310 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Copyright terms: Public domain | W3C validator |