Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > coeq2i | GIF version |
Description: Equality inference for composition of two classes. (Contributed by NM, 16-Nov-2000.) |
Ref | Expression |
---|---|
coeq1i.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
coeq2i | ⊢ (𝐶 ∘ 𝐴) = (𝐶 ∘ 𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coeq1i.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | coeq2 4756 | . 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 1342 ∘ ccom 4602 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-in 3117 df-ss 3124 df-br 3977 df-opab 4038 df-co 4607 |
This theorem is referenced by: coeq12i 4761 cocnvcnv2 5109 co01 5112 cocnvres 5122 fcoi1 5362 dftpos2 6220 tposco 6234 |
Copyright terms: Public domain | W3C validator |