![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > eqeq12i | Unicode version |
Description: A useful inference for substituting definitions into an equality. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) |
Ref | Expression |
---|---|
eqeq12i.1 |
![]() ![]() ![]() ![]() |
eqeq12i.2 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
eqeq12i |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq12i.1 |
. 2
![]() ![]() ![]() ![]() | |
2 | eqeq12i.2 |
. 2
![]() ![]() ![]() ![]() | |
3 | eqeq12 2190 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 1, 2, 3 | mp2an 426 |
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-5 1447 ax-gen 1449 ax-4 1510 ax-17 1526 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 |
This theorem is referenced by: rabbi 2654 sbceqg 3073 preqr2g 3767 preqr2 3769 otth 4242 rncoeq 4900 eqfnov 5980 mpo2eqb 5983 f1o2ndf1 6228 ecopovsym 6630 sq11i 10609 pwle2 14718 |
Copyright terms: Public domain | W3C validator |