Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > difeq1i | GIF version |
Description: Inference adding difference to the right in a class equality. (Contributed by NM, 15-Nov-2002.) |
Ref | Expression |
---|---|
difeq1i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
difeq1i | ⊢ (𝐴 ∖ 𝐶) = (𝐵 ∖ 𝐶) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | difeq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | difeq1 3187 | . 2 ⊢ (𝐴 = 𝐵 → (𝐴 ∖ 𝐶) = (𝐵 ∖ 𝐶)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐴 ∖ 𝐶) = (𝐵 ∖ 𝐶) |
Colors of variables: wff set class |
Syntax hints: = wceq 1331 ∖ cdif 3068 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-rab 2425 df-dif 3073 |
This theorem is referenced by: difeq12i 3192 indif1 3321 indifcom 3322 difun1 3336 notab 3346 notrab 3353 difprsn1 3659 difprsn2 3660 orddif 4462 resdifcom 4837 resdmdfsn 4862 phplem1 6746 dfn2 8990 |
Copyright terms: Public domain | W3C validator |