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Mirrors > Home > MPE Home > Th. List > Mathboxes > elabrexg | Structured version Visualization version Unicode version |
Description: Elementhood in an image set. (Contributed by Glauco Siliprandi, 11-Dec-2019.) |
Ref | Expression |
---|---|
elabrexg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1487 | . . . . 5 | |
2 | csbeq1a 3542 | . . . . . . . 8 | |
3 | 2 | equcoms 1947 | . . . . . . 7 |
4 | a1tru 1500 | . . . . . . 7 | |
5 | 3, 4 | 2thd 255 | . . . . . 6 |
6 | 5 | rspcev 3309 | . . . . 5 |
7 | 1, 6 | mpan2 707 | . . . 4 |
8 | 7 | adantr 481 | . . 3 |
9 | eqeq1 2626 | . . . . . 6 | |
10 | 9 | rexbidv 3052 | . . . . 5 |
11 | 10 | elabg 3351 | . . . 4 |
12 | 11 | adantl 482 | . . 3 |
13 | 8, 12 | mpbird 247 | . 2 |
14 | nfv 1843 | . . . 4 | |
15 | nfcsb1v 3549 | . . . . 5 | |
16 | 15 | nfeq2 2780 | . . . 4 |
17 | 2 | eqeq2d 2632 | . . . 4 |
18 | 14, 16, 17 | cbvrex 3168 | . . 3 |
19 | 18 | abbii 2739 | . 2 |
20 | 13, 19 | syl6eleqr 2712 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wtru 1484 wcel 1990 cab 2608 wrex 2913 csb 3533 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-v 3202 df-sbc 3436 df-csb 3534 |
This theorem is referenced by: upbdrech 39519 ssfiunibd 39523 |
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