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Mirrors > Home > ILE Home > Th. List > bcxmaslem1 | GIF version |
Description: Lemma for bcxmas 11398. (Contributed by Paul Chapman, 18-May-2007.) |
Ref | Expression |
---|---|
bcxmaslem1 | ⊢ (𝐴 = 𝐵 → ((𝑁 + 𝐴)C𝐴) = ((𝑁 + 𝐵)C𝐵)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq2 5835 | . 2 ⊢ (𝐴 = 𝐵 → (𝑁 + 𝐴) = (𝑁 + 𝐵)) | |
2 | id 19 | . 2 ⊢ (𝐴 = 𝐵 → 𝐴 = 𝐵) | |
3 | 1, 2 | oveq12d 5845 | 1 ⊢ (𝐴 = 𝐵 → ((𝑁 + 𝐴)C𝐴) = ((𝑁 + 𝐵)C𝐵)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 = wceq 1335 (class class class)co 5827 + caddc 7738 Ccbc 10633 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 df-un 3106 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-iota 5138 df-fv 5181 df-ov 5830 |
This theorem is referenced by: bcxmas 11398 |
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