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Mirrors > Home > MPE Home > Th. List > ss2rabi | Structured version Visualization version Unicode version |
Description: Inference of restricted abstraction subclass from implication. (Contributed by NM, 14-Oct-1999.) |
Ref | Expression |
---|---|
ss2rabi.1 |
Ref | Expression |
---|---|
ss2rabi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ss2rab 3678 | . 2 | |
2 | ss2rabi.1 | . 2 | |
3 | 1, 2 | mprgbir 2927 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 crab 2916 wss 3574 |
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-ral 2917 df-rab 2921 df-in 3581 df-ss 3588 |
This theorem is referenced by: supub 8365 suplub 8366 card2on 8459 rankval4 8730 fin1a2lem12 9233 catlid 16344 catrid 16345 gsumval2 17280 lbsextlem3 19160 psrbagsn 19495 musum 24917 ppiub 24929 umgrupgr 25998 umgrislfupgr 26018 usgruspgr 26073 usgrislfuspgr 26079 disjxwwlksn 26799 clwwlknclwwlkdifnum 26874 konigsbergssiedgw 27111 omssubadd 30362 bj-unrab 32922 poimirlem26 33435 poimirlem27 33436 lclkrs2 36829 |
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