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Mirrors > Home > MPE Home > Th. List > brwitnlem | Structured version Visualization version Unicode version |
Description: Lemma for relations which assert the existence of a witness in a two-parameter set. (Contributed by Stefan O'Rear, 25-Jan-2015.) (Revised by Mario Carneiro, 23-Aug-2015.) |
Ref | Expression |
---|---|
brwitnlem.r | |
brwitnlem.o |
Ref | Expression |
---|---|
brwitnlem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvex 6201 | . . . . 5 | |
2 | dif1o 7580 | . . . . 5 | |
3 | 1, 2 | mpbiran 953 | . . . 4 |
4 | 3 | anbi2i 730 | . . 3 |
5 | brwitnlem.o | . . . 4 | |
6 | elpreima 6337 | . . . 4 | |
7 | 5, 6 | ax-mp 5 | . . 3 |
8 | ndmfv 6218 | . . . . . 6 | |
9 | 8 | necon1ai 2821 | . . . . 5 |
10 | fndm 5990 | . . . . . 6 | |
11 | 5, 10 | ax-mp 5 | . . . . 5 |
12 | 9, 11 | syl6eleq 2711 | . . . 4 |
13 | 12 | pm4.71ri 665 | . . 3 |
14 | 4, 7, 13 | 3bitr4i 292 | . 2 |
15 | brwitnlem.r | . . . 4 | |
16 | 15 | breqi 4659 | . . 3 |
17 | df-br 4654 | . . 3 | |
18 | 16, 17 | bitri 264 | . 2 |
19 | df-ov 6653 | . . 3 | |
20 | 19 | neeq1i 2858 | . 2 |
21 | 14, 18, 20 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wceq 1483 wcel 1990 wne 2794 cvv 3200 cdif 3571 c0 3915 cop 4183 class class class wbr 4653 ccnv 5113 cdm 5114 cima 5117 wfn 5883 cfv 5888 (class class class)co 6650 c1o 7553 |
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-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 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-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-id 5024 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-suc 5729 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 df-ov 6653 df-1o 7560 |
This theorem is referenced by: brgic 17711 brric 18744 brlmic 19068 hmph 21579 |
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