![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > equid | Unicode version |
Description: Identity law for equality
(reflexivity). Lemma 6 of [Tarski] p. 68.
This is often an axiom of equality in textbook systems, but we don't
need it as an axiom since it can be proved from our other axioms.
This proof is similar to Tarski's and makes use of a dummy variable
|
Ref | Expression |
---|---|
equid |
![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1627 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() | |
2 | ax-17 1460 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | ax-8 1436 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 3 | pm2.43i 48 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 2, 4 | exlimih 1525 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | 1, 5 | ax-mp 7 |
1
![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-gen 1379 ax-ie2 1424 ax-8 1436 ax-17 1460 ax-i9 1464 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: nfequid 1631 stdpc6 1632 equcomi 1633 equveli 1684 sbid 1699 ax16i 1781 exists1 2039 vjust 2611 vex 2613 reu6 2791 nfccdeq 2823 sbc8g 2832 dfnul3 3271 rab0 3290 int0 3671 ruv 4322 relop 4535 f1eqcocnv 5483 mpt2xopoveq 5910 |
Copyright terms: Public domain | W3C validator |