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Mathbox for Stefan O'Rear |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > frlmrcl | Unicode version |
Description: If a free module is inhabited, this is sufficient to conclude that the ring expression defines a set. (Contributed by Stefan O'Rear, 3-Feb-2015.) |
Ref | Expression |
---|---|
frlmval.f |
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frlmrcl.b |
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Ref | Expression |
---|---|
frlmrcl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frlmval.f |
. 2
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2 | frlmrcl.b |
. 2
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3 | df-frlm 27082 |
. . 3
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4 | 3 | reldmmpt2 6140 |
. 2
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5 | 1, 2, 4 | strov2rcl 16586 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: frlmbassup 27094 frlmbasmap 27095 frlmvscafval 27098 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-13 1723 ax-14 1725 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2385 ax-sep 4290 ax-nul 4298 ax-pow 4337 ax-pr 4363 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3an 938 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-eu 2258 df-mo 2259 df-clab 2391 df-cleq 2397 df-clel 2400 df-nfc 2529 df-ne 2569 df-ral 2671 df-rex 2672 df-rab 2675 df-v 2918 df-sbc 3122 df-dif 3283 df-un 3285 df-in 3287 df-ss 3294 df-nul 3589 df-if 3700 df-sn 3780 df-pr 3781 df-op 3783 df-uni 3976 df-br 4173 df-opab 4227 df-mpt 4228 df-id 4458 df-xp 4843 df-rel 4844 df-cnv 4845 df-co 4846 df-dm 4847 df-iota 5377 df-fun 5415 df-fv 5421 df-ov 6043 df-oprab 6044 df-mpt2 6045 df-slot 13428 df-base 13429 df-frlm 27082 |
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