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 2170 | . 2 | |
4 | 1, 2, 3 | mp2an 423 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1335 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1427 ax-gen 1429 ax-4 1490 ax-17 1506 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-cleq 2150 |
This theorem is referenced by: rabbi 2634 sbceqg 3047 preqr2g 3731 preqr2 3733 otth 4203 rncoeq 4860 eqfnov 5928 mpo2eqb 5931 f1o2ndf1 6176 ecopovsym 6577 sq11i 10512 pwle2 13612 |
Copyright terms: Public domain | W3C validator |