![]() |
Higher-Order Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > HOLE Home > Th. List > mpdan | Unicode version |
Description: Modus ponens deduction. (Contributed by Mario Carneiro, 8-Oct-2014.) |
Ref | Expression |
---|---|
mpdan.1 |
![]() ![]() ![]() ![]() |
mpdan.2 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
mpdan |
![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mpdan.1 |
. . . 4
![]() ![]() ![]() ![]() | |
2 | 1 | ax-cb1 29 |
. . 3
![]() ![]() ![]() ![]() |
3 | 2 | id 25 |
. 2
![]() ![]() ![]() ![]() |
4 | mpdan.2 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 3, 1, 4 | syl2anc 19 |
1
![]() ![]() ![]() ![]() |
Colors of variables: type var term |
Syntax hints: kct 10
![]() |
This theorem was proved from axioms: ax-syl 15 ax-jca 17 ax-id 24 ax-cb1 29 |
This theorem is referenced by: hbov 111 hbct 155 |
Copyright terms: Public domain | W3C validator |