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Mirrors > Home > MPE Home > Th. List > funimass3 | Structured version Visualization version Unicode version |
Description: A kind of contraposition
law that infers an image subclass from a
subclass of a preimage. Raph Levien remarks: "Likely this could
be
proved directly, and fvimacnv 5997 would be the special case of ![]() |
Ref | Expression |
---|---|
funimass3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funimass4 5916 |
. . 3
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2 | ssel 3426 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | fvimacnv 5997 |
. . . . . . 7
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4 | 3 | ex 436 |
. . . . . 6
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5 | 2, 4 | syl9r 74 |
. . . . 5
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6 | 5 | imp31 434 |
. . . 4
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7 | 6 | ralbidva 2824 |
. . 3
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8 | 1, 7 | bitrd 257 |
. 2
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9 | dfss3 3422 |
. 2
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10 | 8, 9 | syl6bbr 267 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-sep 4525 ax-nul 4534 ax-pr 4639 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3047 df-sbc 3268 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-br 4403 df-opab 4462 df-id 4749 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 df-iota 5546 df-fun 5584 df-fn 5585 df-fv 5590 |
This theorem is referenced by: funimass5 5999 funconstss 6000 fvimacnvALT 6001 fimacnv 6012 r0weon 8443 iscnp3 20260 cnpnei 20280 cnclsi 20288 cncls 20290 cncnp 20296 1stccnp 20477 txcnpi 20623 xkoco2cn 20673 xkococnlem 20674 basqtop 20726 kqnrmlem1 20758 kqnrmlem2 20759 reghmph 20808 nrmhmph 20809 elfm3 20965 rnelfm 20968 symgtgp 21116 tgpconcompeqg 21126 eltsms 21147 ucnprima 21297 plyco0 23146 plyeq0 23165 xrlimcnp 23894 rinvf1o 28230 xppreima 28248 cvmliftmolem1 30004 cvmlift2lem9 30034 cvmlift3lem6 30047 mclsppslem 30221 |
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