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Mirrors > Home > MPE Home > Th. List > Mathboxes > elno2 | Structured version Visualization version Unicode version |
Description: An alternative condition for membership in . (Contributed by Scott Fenton, 21-Mar-2012.) |
Ref | Expression |
---|---|
elno2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nofun 31802 | . . 3 | |
2 | nodmon 31803 | . . 3 | |
3 | norn 31804 | . . 3 | |
4 | 1, 2, 3 | 3jca 1242 | . 2 |
5 | simp2 1062 | . . . 4 | |
6 | simpl 473 | . . . . . . . 8 | |
7 | eqidd 2623 | . . . . . . . 8 | |
8 | df-fn 5891 | . . . . . . . 8 | |
9 | 6, 7, 8 | sylanbrc 698 | . . . . . . 7 |
10 | 9 | anim1i 592 | . . . . . 6 |
11 | 10 | 3impa 1259 | . . . . 5 |
12 | df-f 5892 | . . . . 5 | |
13 | 11, 12 | sylibr 224 | . . . 4 |
14 | feq2 6027 | . . . . 5 | |
15 | 14 | rspcev 3309 | . . . 4 |
16 | 5, 13, 15 | syl2anc 693 | . . 3 |
17 | elno 31799 | . . 3 | |
18 | 16, 17 | sylibr 224 | . 2 |
19 | 4, 18 | impbii 199 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 wrex 2913 wss 3574 cpr 4179 cdm 5114 crn 5115 con0 5723 wfun 5882 wfn 5883 wf 5884 c1o 7553 c2o 7554 csur 31793 |
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 ax-rep 4771 ax-sep 4781 ax-nul 4789 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-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-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 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-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-no 31796 |
This theorem is referenced by: elno3 31808 noextend 31819 noextendseq 31820 nosupno 31849 |
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