Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > eldifpr | Structured version Visualization version Unicode version |
Description: Membership in a set with two elements removed. Similar to eldifsn 4317 and eldiftp 4228. (Contributed by Mario Carneiro, 18-Jul-2017.) |
Ref | Expression |
---|---|
eldifpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elprg 4196 | . . . . 5 | |
2 | 1 | notbid 308 | . . . 4 |
3 | neanior 2886 | . . . 4 | |
4 | 2, 3 | syl6bbr 278 | . . 3 |
5 | 4 | pm5.32i 669 | . 2 |
6 | eldif 3584 | . 2 | |
7 | 3anass 1042 | . 2 | |
8 | 5, 6, 7 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 wo 383 wa 384 w3a 1037 wceq 1483 wcel 1990 wne 2794 cdif 3571 cpr 4179 |
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-3an 1039 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-ne 2795 df-v 3202 df-dif 3577 df-un 3579 df-sn 4178 df-pr 4180 |
This theorem is referenced by: rexdifpr 4205 logbcl 24505 logbid1 24506 logb1 24507 elogb 24508 logbchbase 24509 relogbval 24510 relogbcl 24511 relogbreexp 24513 relogbmul 24515 relogbexp 24518 nnlogbexp 24519 relogbcxp 24523 cxplogb 24524 relogbcxpb 24525 logbmpt 24526 logbfval 24528 eluz2cnn0n1 42301 rege1logbrege0 42352 relogbmulbexp 42355 relogbdivb 42356 nnpw2blen 42374 |
Copyright terms: Public domain | W3C validator |