![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 3580 | . 2 ⊢ (A = B → ∪ A = ∪ B) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ ∪ A = ∪ B |
Colors of variables: wff set class |
Syntax hints: = wceq 1242 ∪ cuni 3571 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-nfc 2164 df-rex 2306 df-uni 3572 |
This theorem is referenced by: elunirab 3584 unisn 3587 uniop 3983 unisuc 4116 unisucg 4117 univ 4173 dfiun3g 4532 op1sta 4745 op2nda 4748 dfdm2 4795 iotajust 4809 dfiota2 4811 cbviota 4815 sb8iota 4817 dffv4g 5118 funfvdm2f 5181 riotauni 5417 1st0 5713 2nd0 5714 unielxp 5742 brtpos0 5808 recsfval 5872 uniqs 6100 xpassen 6240 |
Copyright terms: Public domain | W3C validator |