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Mirrors > Home > NFE Home > Th. List > unieq | Unicode version |
Description: Equality theorem for class union. Exercise 15 of [TakeutiZaring] p. 18. (Contributed by NM, 10-Aug-1993.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
unieq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexeq 2808 | . . 3 | |
2 | 1 | abbidv 2467 | . 2 |
3 | dfuni2 3893 | . 2 | |
4 | dfuni2 3893 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2410 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1642 wcel 1710 cab 2339 wrex 2615 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-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: unieqi 3901 unieqd 3902 uniintsn 3963 iununi 4050 pw1equn 4331 pw1eqadj 4332 nnadjoin 4520 pw1fnval 5851 pw1fnf1o 5855 brtcfn 6246 |
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