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 3610 | . 2 ⊢ (𝐴 = 𝐵 → ∪ 𝐴 = ∪ 𝐵) | |
3 | 1, 2 | ax-mp 7 | 1 ⊢ ∪ 𝐴 = ∪ 𝐵 |
Colors of variables: wff set class |
Syntax hints: = wceq 1284 ∪ cuni 3601 |
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 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rex 2354 df-uni 3602 |
This theorem is referenced by: elunirab 3614 unisn 3617 uniop 4010 unisuc 4168 unisucg 4169 univ 4225 dfiun3g 4607 op1sta 4822 op2nda 4825 dfdm2 4872 iotajust 4886 dfiota2 4888 cbviota 4892 sb8iota 4894 dffv4g 5195 funfvdm2f 5259 riotauni 5494 1st0 5791 2nd0 5792 unielxp 5820 brtpos0 5890 recsfval 5954 uniqs 6187 xpassen 6327 sup00 6416 |
Copyright terms: Public domain | W3C validator |