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Mirrors > Home > MPE Home > Th. List > alrimi | Structured version Visualization version GIF version |
Description: Inference form of Theorem 19.21 of [Margaris] p. 90, see 19.21 2201. (Contributed by Mario Carneiro, 24-Sep-2016.) |
Ref | Expression |
---|---|
alrimi.1 | ⊢ Ⅎ𝑥𝜑 |
alrimi.2 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
alrimi | ⊢ (𝜑 → ∀𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | alrimi.1 | . . 3 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | nf5ri 2189 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) |
3 | alrimi.2 | . 2 ⊢ (𝜑 → 𝜓) | |
4 | 2, 3 | alrimih 1827 | 1 ⊢ (𝜑 → ∀𝑥𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1540 Ⅎwnf 1786 |
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 ax-6 1972 ax-7 2012 ax-12 2172 |
This theorem depends on definitions: df-bi 206 df-ex 1783 df-nf 1787 |
This theorem is referenced by: sbimd 2238 sbbid 2239 nf5d 2281 axc4i 2316 19.12 2321 nfsbd 2522 mobid 2545 mo3 2559 eubid 2582 2moexv 2624 eupicka 2631 2moex 2637 2mo 2645 abbid 2804 nfcd 2892 nfabdwOLD 2928 ceqsalgALT 3509 ceqsexOLD 3525 vtocldf 3542 rspcdf 3600 elrab3t 3683 morex 3716 sbciedf 3822 csbiebt 3924 csbiedf 3925 ssrd 3988 eqrd 4002 invdisj 5133 zfrepclf 5295 eusv2nf 5394 ssopab2bw 5548 ssopab2b 5550 imadif 6633 eusvobj1 7402 ssoprab2b 7478 eqoprab2bw 7479 ovmpodxf 7558 axrepnd 10589 axunnd 10591 axpownd 10596 axregndlem1 10597 axacndlem1 10602 axacndlem2 10603 axacndlem3 10604 axacndlem4 10605 axacndlem5 10606 axacnd 10607 mreexexd 17592 acsmapd 18507 isch3 30494 ssrelf 31844 eqrelrd2 31845 esumeq12dvaf 33029 bnj1366 33840 bnj571 33917 bnj964 33954 iota5f 34693 bj-hbext 35588 bj-nfext 35590 wl-mo3t 36441 wl-ax11-lem3 36449 cover2 36583 alrimii 36987 mpobi123f 37030 mptbi12f 37034 ss2iundf 42410 pm11.57 43148 pm11.59 43150 tratrb 43297 hbexg 43317 e2ebindALT 43690 mpteq1dfOLD 43939 mpteq12daOLD 43946 dvnmul 44659 stoweidlem34 44750 sge0fodjrnlem 45132 pimrecltpos 45424 pimrecltneg 45440 smfaddlem1 45479 smfresal 45504 smfinflem 45533 smfinfmpt 45535 ichnfim 46132 ovmpordxf 47014 setrec1lem4 47735 |
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