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Mirrors > Home > NFE Home > Th. List > uniss | Unicode version |
Description: Subclass relationship for class union. Theorem 61 of [Suppes] p. 39. (Contributed by NM, 22-Mar-1998.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
uniss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3267 | . . . . 5 | |
2 | 1 | anim2d 548 | . . . 4 |
3 | 2 | eximdv 1622 | . . 3 |
4 | eluni 3894 | . . 3 | |
5 | eluni 3894 | . . 3 | |
6 | 3, 4, 5 | 3imtr4g 261 | . 2 |
7 | 6 | ssrdv 3278 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 wex 1541 wcel 1710 wss 3257 cuni 3891 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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-in 3213 df-ss 3259 df-uni 3892 |
This theorem is referenced by: unissi 3914 unissd 3915 unidif 3923 intssuni2 3951 uniintsn 3963 sspw1 4335 |
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