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Mirrors > Home > MPE Home > Th. List > eusvobj1 | Structured version Visualization version Unicode version |
Description: Specify the same object in two ways when class is single-valued. (Contributed by NM, 1-Nov-2010.) (Proof shortened by Mario Carneiro, 19-Nov-2016.) |
Ref | Expression |
---|---|
eusvobj1.1 |
Ref | Expression |
---|---|
eusvobj1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfeu1 2480 | . . 3 | |
2 | eusvobj1.1 | . . . 4 | |
3 | 2 | eusvobj2 6643 | . . 3 |
4 | 1, 3 | alrimi 2082 | . 2 |
5 | iotabi 5860 | . 2 | |
6 | 4, 5 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wal 1481 wceq 1483 wcel 1990 weu 2470 wral 2912 wrex 2913 cvv 3200 cio 5849 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-nul 3916 df-sn 4178 df-uni 4437 df-iota 5851 |
This theorem is referenced by: (None) |
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