New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > coeq2i | GIF version |
Description: Equality inference for composition of two classes. (Contributed by set.mm contributors, 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 4875 | . 2 ⊢ (A = B → (C ∘ A) = (C ∘ B)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (C ∘ A) = (C ∘ B) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1642 ∘ ccom 4721 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259 df-opab 4623 df-br 4640 df-co 4726 |
This theorem is referenced by: coeq12i 4880 coi2 5095 funi 5137 f1ococnv1 5310 |
Copyright terms: Public domain | W3C validator |