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Mirrors > Home > MPE Home > Th. List > Mathboxes > hfext | Structured version Visualization version Unicode version |
Description: Extensionality for HF sets depends only on comparison of HF elements. (Contributed by Scott Fenton, 16-Jul-2015.) |
Ref | Expression |
---|---|
hfext | Hf Hf Hf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3203 | . . . . . 6 | |
2 | eldif 3584 | . . . . . 6 Hf Hf | |
3 | 1, 2 | mpbiran 953 | . . . . 5 Hf Hf |
4 | hfelhf 32288 | . . . . . . . 8 Hf Hf | |
5 | 4 | stoic1b 1698 | . . . . . . 7 Hf Hf |
6 | 5 | adantlr 751 | . . . . . 6 Hf Hf Hf |
7 | hfelhf 32288 | . . . . . . . 8 Hf Hf | |
8 | 7 | stoic1b 1698 | . . . . . . 7 Hf Hf |
9 | 8 | adantll 750 | . . . . . 6 Hf Hf Hf |
10 | 6, 9 | 2falsed 366 | . . . . 5 Hf Hf Hf |
11 | 3, 10 | sylan2b 492 | . . . 4 Hf Hf Hf |
12 | 11 | ralrimiva 2966 | . . 3 Hf Hf Hf |
13 | 12 | biantrud 528 | . 2 Hf Hf Hf Hf Hf |
14 | dfcleq 2616 | . . 3 | |
15 | unvdif 4042 | . . . . 5 Hf Hf | |
16 | 15 | raleqi 3142 | . . . 4 Hf Hf |
17 | ralv 3219 | . . . 4 | |
18 | 16, 17 | bitr2i 265 | . . 3 Hf Hf |
19 | ralunb 3794 | . . 3 Hf Hf Hf Hf | |
20 | 14, 18, 19 | 3bitri 286 | . 2 Hf Hf |
21 | 13, 20 | syl6rbbr 279 | 1 Hf Hf Hf |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wa 384 wal 1481 wceq 1483 wcel 1990 wral 2912 cvv 3200 cdif 3571 cun 3572 Hf chf 32279 |
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-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-rep 4771 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 ax-reg 8497 ax-inf2 8538 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-pss 3590 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-tp 4182 df-op 4184 df-uni 4437 df-int 4476 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-tr 4753 df-id 5024 df-eprel 5029 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-pred 5680 df-ord 5726 df-on 5727 df-lim 5728 df-suc 5729 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-om 7066 df-wrecs 7407 df-recs 7468 df-rdg 7506 df-er 7742 df-en 7956 df-dom 7957 df-sdom 7958 df-r1 8627 df-rank 8628 df-hf 32280 |
This theorem is referenced by: (None) |
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