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Mirrors > Home > MPE Home > Th. List > albidv | Structured version Visualization version GIF version |
Description: Formula-building rule for universal quantifier (deduction form). See also albidh 1870 and albid 2216. (Contributed by NM, 26-May-1993.) |
Ref | Expression |
---|---|
albidv.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
albidv | ⊢ (𝜑 → (∀𝑥𝜓 ↔ ∀𝑥𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-5 1914 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | albidv.1 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
3 | 1, 2 | albidh 1870 | 1 ⊢ (𝜑 → (∀𝑥𝜓 ↔ ∀𝑥𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 205 ∀wal 1540 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 |
This theorem depends on definitions: df-bi 206 |
This theorem is referenced by: nfbidv 1926 2albidv 1927 sbjust 2067 sbequ 2087 sb6 2089 ax12wdemo 2132 sb4b 2475 mojust 2534 mof 2558 eujust 2566 eujustALT 2567 eu6lem 2568 euf 2571 axextg 2706 axextmo 2708 eqeq1dALT 2736 nfcriOLD 2894 nfceqdf 2899 nfceqdfOLD 2900 drnfc1 2923 drnfc1OLD 2924 drnfc2 2925 drnfc2OLD 2926 ralbidv2 3174 ralxpxfr2d 3635 alexeqg 3640 pm13.183 3657 elab6g 3660 elabd2 3661 eqeu 3703 mo2icl 3711 euind 3721 reuind 3750 cdeqal 3766 sbcal 3842 sbcabel 3873 csbiebg 3927 ssconb 4138 reldisj 4452 reldisjOLD 4453 sbcssg 4524 elint 4957 axrep1 5287 axreplem 5288 axrep2 5289 axrep4 5291 zfrepclf 5295 axsepg 5301 zfauscl 5302 bm1.3ii 5303 al0ssb 5309 eusv1 5390 euotd 5514 freq1 5647 frsn 5764 iota5 6527 dffun2 6554 sbcfung 6573 funimass4 6957 dffo3 7104 eufnfv 7231 dff13 7254 fnssintima 7359 nfriotadw 7373 imaeqalov 7646 tfisi 7848 dfom2 7857 elom 7858 xpord3inddlem 8140 seqomlem2 8451 findcard 9163 findcard2 9164 pssnn 9168 ssfi 9173 pssnnOLD 9265 findcard2OLD 9284 findcard3 9285 findcard3OLD 9286 fiint 9324 inf0 9616 axinf2 9635 ttrclss 9715 ttrclselem2 9721 tz9.1 9724 karden 9890 aceq0 10113 dfac5 10123 zfac 10455 brdom3 10523 axpowndlem3 10594 zfcndrep 10609 zfcndac 10614 elgch 10617 engch 10623 axgroth3 10826 axgroth4 10827 elnp 10982 elnpi 10983 infm3 12173 fz1sbc 13577 uzrdgfni 13923 trclfvcotr 14956 relexpindlem 15010 vdwmc2 16912 ramtlecl 16933 ramval 16941 ramub 16946 rami 16948 ramcl 16962 mreexexd 17592 mplsubglem 21558 mpllsslem 21559 ismhp3 21686 istopg 22397 1stccn 22967 iskgen3 23053 fbfinnfr 23345 cnextfun 23568 metcld 24823 metcld2 24824 chlimi 30518 nmcexi 31310 disjxun0 31836 disjrdx 31853 funcnvmpt 31923 mclsssvlem 34584 mclsval 34585 mclsind 34592 elintfv 34767 dfon2lem6 34791 dfon2lem7 34792 dfon2lem8 34793 dfon2 34795 sscoid 34916 trer 35249 bj-ssblem1 35579 bj-ax12 35582 mobidvALT 35784 bj-sbceqgALT 35830 bj-nuliota 35986 bj-bm1.3ii 35993 wl-mo2t 36488 isass 36762 releccnveq 37174 ecin0 37269 inecmo 37272 alrmomodm 37276 extssr 37427 eltrrels3 37498 eleqvrels3 37511 axc11n-16 37856 cdlemefrs29bpre0 39315 unielss 42015 orddif0suc 42066 elmapintab 42395 cnvcnvintabd 42399 iunrelexpuztr 42518 ntrneiiso 42890 ntrneik2 42891 ntrneix2 42892 ntrneikb 42893 mnuop123d 43069 pm14.122b 43230 iotavalb 43237 trsbc 43349 dffo3f 43925 eusnsn 45784 aiota0def 45852 ichbidv 46169 mof0 47552 eufsnlem 47555 setrecseq 47778 setrec1lem1 47780 setrec2fun 47785 setrec2lem2 47787 |
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