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Mirrors > Home > MPE Home > Th. List > cnvss | Structured version Visualization version Unicode version |
Description: Subset theorem for converse. (Contributed by NM, 22-Mar-1998.) |
Ref | Expression |
---|---|
cnvss |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3438 |
. . . 4
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2 | df-br 4419 |
. . . 4
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3 | df-br 4419 |
. . . 4
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4 | 1, 2, 3 | 3imtr4g 278 |
. . 3
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5 | 4 | ssopab2dv 4747 |
. 2
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6 | df-cnv 4864 |
. 2
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7 | df-cnv 4864 |
. 2
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8 | 5, 6, 7 | 3sstr4g 3485 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-in 3423 df-ss 3430 df-br 4419 df-opab 4478 df-cnv 4864 |
This theorem is referenced by: cnveq 5030 rnss 5085 relcnvtr 5378 funss 5623 funres11 5677 funcnvres 5678 foimacnv 5858 funcnvuni 6778 tposss 7005 vdwnnlem1 15000 structcnvcnv 15187 catcoppccl 16058 cnvps 16513 tsrdir 16539 ustneism 21293 metustsym 21625 metust 21628 pi1xfrcnv 22143 eulerpartlemmf 29258 cnvssb 36238 trclubgNEW 36271 clrellem 36275 clcnvlem 36276 cnvrcl0 36278 cnvtrcl0 36279 cnvtrrel 36308 relexpaddss 36356 |
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