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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 3662 | . 2 ⊢ (𝐴 = 𝐵 → ∪ 𝐴 = ∪ 𝐵) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ ∪ 𝐴 = ∪ 𝐵 |
Colors of variables: wff set class |
Syntax hints: = wceq 1289 ∪ cuni 3653 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-rex 2365 df-uni 3654 |
This theorem is referenced by: elunirab 3666 unisn 3669 uniop 4082 unisuc 4240 unisucg 4241 univ 4298 dfiun3g 4690 op1sta 4912 op2nda 4915 dfdm2 4965 iotajust 4979 dfiota2 4981 cbviota 4985 sb8iota 4987 dffv4g 5302 funfvdm2f 5369 riotauni 5614 1st0 5915 2nd0 5916 unielxp 5944 brtpos0 6017 recsfval 6080 uniqs 6348 xpassen 6544 sup00 6696 |
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