Mathbox for Mario Carneiro |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > subfacval | Structured version Visualization version Unicode version |
Description: The subfactorial is defined as the number of derangements (see derangval 31149) of the set . (Contributed by Mario Carneiro, 21-Jan-2015.) |
Ref | Expression |
---|---|
derang.d | |
subfac.n |
Ref | Expression |
---|---|
subfacval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oveq2 6658 | . . 3 | |
2 | 1 | fveq2d 6195 | . 2 |
3 | subfac.n | . 2 | |
4 | fvex 6201 | . 2 | |
5 | 2, 3, 4 | fvmpt 6282 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cab 2608 wne 2794 wral 2912 cmpt 4729 wf1o 5887 cfv 5888 (class class class)co 6650 cfn 7955 c1 9937 cn0 11292 cfz 12326 chash 13117 |
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-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-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-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 |
This theorem is referenced by: derangen2 31156 subfaclefac 31158 subfac0 31159 subfac1 31160 subfacp1lem6 31167 |
Copyright terms: Public domain | W3C validator |