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Mirrors > Home > ILE Home > Th. List > unieqi | GIF version |
Description: Inference of equality of two class unions. (Contributed by NM, 30-Aug-1993.) |
Ref | Expression |
---|---|
unieqi.1 | ⊢ 𝐴 = 𝐵 |
Ref | Expression |
---|---|
unieqi | ⊢ ∪ 𝐴 = ∪ 𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | unieqi.1 | . 2 ⊢ 𝐴 = 𝐵 | |
2 | unieq 3745 | . 2 ⊢ (𝐴 = 𝐵 → ∪ 𝐴 = ∪ 𝐵) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∪ 𝐴 = ∪ 𝐵 |
Colors of variables: wff set class |
Syntax hints: = wceq 1331 ∪ cuni 3736 |
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-rex 2422 df-uni 3737 |
This theorem is referenced by: elunirab 3749 unisn 3752 uniop 4177 unisuc 4335 unisucg 4336 univ 4397 dfiun3g 4796 op1sta 5020 op2nda 5023 dfdm2 5073 iotajust 5087 dfiota2 5089 cbviota 5093 sb8iota 5095 dffv4g 5418 funfvdm2f 5486 riotauni 5736 1st0 6042 2nd0 6043 unielxp 6072 brtpos0 6149 recsfval 6212 uniqs 6487 xpassen 6724 sup00 6890 suplocexprlemell 7521 uptx 12443 |
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