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Mirrors > Home > MPE Home > Th. List > prpssnq | Structured version Visualization version Unicode version |
Description: A positive real is a subset of the positive fractions. (Contributed by NM, 29-Feb-1996.) (Revised by Mario Carneiro, 11-May-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
prpssnq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elnpi 9810 | . 2 | |
2 | simpl3 1066 | . 2 | |
3 | 1, 2 | sylbi 207 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wal 1481 wcel 1990 wral 2912 wrex 2913 cvv 3200 wpss 3575 c0 3915 class class class wbr 4653 cnq 9674 cltq 9680 cnp 9681 |
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-ral 2917 df-rex 2918 df-v 3202 df-in 3581 df-ss 3588 df-pss 3590 df-np 9803 |
This theorem is referenced by: elprnq 9813 npomex 9818 genpnnp 9827 prlem934 9855 ltexprlem2 9859 reclem2pr 9870 suplem1pr 9874 wuncn 9991 |
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