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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 3753 | . 2 ⊢ (𝐴 = 𝐵 → ∪ 𝐴 = ∪ 𝐵) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∪ 𝐴 = ∪ 𝐵 |
Colors of variables: wff set class |
Syntax hints: = wceq 1332 ∪ cuni 3744 |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-uni 3745 |
This theorem is referenced by: elunirab 3757 unisn 3760 uniop 4185 unisuc 4343 unisucg 4344 univ 4405 dfiun3g 4804 op1sta 5028 op2nda 5031 dfdm2 5081 iotajust 5095 dfiota2 5097 cbviota 5101 sb8iota 5103 dffv4g 5426 funfvdm2f 5494 riotauni 5744 1st0 6050 2nd0 6051 unielxp 6080 brtpos0 6157 recsfval 6220 uniqs 6495 xpassen 6732 sup00 6898 suplocexprlemell 7545 uptx 12482 |
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