Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > predss | Structured version Visualization version Unicode version |
Description: The predecessor class of is a subset of . (Contributed by Scott Fenton, 2-Feb-2011.) |
Ref | Expression |
---|---|
predss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-pred 5680 | . 2 | |
2 | inss1 3833 | . 2 | |
3 | 1, 2 | eqsstri 3635 | 1 |
Colors of variables: wff setvar class |
Syntax hints: cin 3573 wss 3574 csn 4177 ccnv 5113 cima 5117 cpred 5679 |
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-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-in 3581 df-ss 3588 df-pred 5680 |
This theorem is referenced by: wfr3g 7413 wfrlem4 7418 wfrlem10 7424 trpredlem1 31727 wsuclem 31773 wsuclemOLD 31774 frr3g 31779 frrlem4 31783 |
Copyright terms: Public domain | W3C validator |