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Mirrors > Home > NFE 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 3900 | . 2 ⊢ (A = B → ∪A = ∪B) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ∪A = ∪B |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1642 ∪cuni 3891 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-rex 2620 df-uni 3892 |
This theorem is referenced by: elunirab 3904 unisn 3907 iotajust 4338 dfiota2 4340 cbviota 4344 sb8iota 4346 dfiota4 4372 op1sta 5072 opswap 5074 op2nda 5076 funfv2 5376 funfv2f 5377 fvco2 5382 funiunfv 5467 elunirn 5470 uniqs 5984 |
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