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Mirrors > Home > NFE Home > Th. List > uneq2 | Unicode version |
Description: Equality theorem for the union of two classes. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
uneq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uneq1 3411 | . 2 | |
2 | uncom 3408 | . 2 | |
3 | uncom 3408 | . 2 | |
4 | 1, 2, 3 | 3eqtr4g 2410 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1642 cun 3207 |
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-nan 1288 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-v 2861 df-nin 3211 df-compl 3212 df-un 3214 |
This theorem is referenced by: uneq12 3413 uneq2i 3415 uneq2d 3418 uneqin 3506 disjssun 3608 uniprg 3906 eladdci 4399 addcid1 4405 elsuc 4413 addcass 4415 phialllem2 4617 cupvalg 5812 |
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