Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > difeq2i | GIF version |
Description: Inference adding difference to the left in a class equality. (Contributed by NM, 15-Nov-2002.) |
Ref | Expression |
---|---|
difeq1i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
difeq2i | ⊢ (𝐶 ∖ 𝐴) = (𝐶 ∖ 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | difeq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | difeq2 3158 | . 2 ⊢ (𝐴 = 𝐵 → (𝐶 ∖ 𝐴) = (𝐶 ∖ 𝐵)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (𝐶 ∖ 𝐴) = (𝐶 ∖ 𝐵) |
Colors of variables: wff set class |
Syntax hints: = wceq 1316 ∖ cdif 3038 |
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-in1 588 ax-in2 589 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-11 1469 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-ral 2398 df-rab 2402 df-dif 3043 |
This theorem is referenced by: difeq12i 3162 inssddif 3287 difdif2ss 3303 dif32 3309 difabs 3310 symdif1 3311 notrab 3323 dif0 3403 difdifdirss 3417 dfif3 3457 difpr 3632 dif1o 6303 unfiin 6782 |
Copyright terms: Public domain | W3C validator |