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Mirrors > Home > MPE Home > Th. List > gen2 | Structured version Visualization version GIF version |
Description: Generalization applied twice. (Contributed by NM, 30-Apr-1998.) |
Ref | Expression |
---|---|
gen2.1 | ⊢ 𝜑 |
Ref | Expression |
---|---|
gen2 | ⊢ ∀𝑥∀𝑦𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | gen2.1 | . . 3 ⊢ 𝜑 | |
2 | 1 | ax-gen 1798 | . 2 ⊢ ∀𝑦𝜑 |
3 | 2 | ax-gen 1798 | 1 ⊢ ∀𝑥∀𝑦𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ∀wal 1540 |
This theorem was proved from axioms: ax-gen 1798 |
This theorem is referenced by: axextmo 2708 moeq 3704 csbie2 3936 mosneq 4844 eusv1 5390 moop2 5503 mosubop 5512 eqrelriv 5790 opabid2 5829 xpidtr 6124 fvmptopabOLD 7464 funoprab 7530 mpofunOLD 7533 fnoprab 7534 elovmpo 7651 wfrfunOLD 8319 tfrlem7 8383 hartogs 9539 card2on 9549 epinid0 9595 cnvepnep 9603 ssttrcl 9710 tskwe 9945 ondomon 10558 fi1uzind 14458 brfi1indALT 14461 climeu 15499 letsr 18546 ulmdm 25905 wlkResOLD 28907 ajmoi 30111 helch 30496 hsn0elch 30501 chintcli 30584 adjmo 31085 nlelchi 31314 hmopidmchi 31404 bnj978 33960 bnj1052 33986 bnj1030 33998 funen1cnv 34091 satfv0 34349 satfv0fun 34362 fnsingle 34891 funimage 34900 funpartfun 34915 imagesset 34925 funtransport 35003 funray 35112 funline 35114 filnetlem3 35265 bj-cbvalimi 35524 bj-cbveximi 35525 ax11-pm 35710 ax11-pm2 35714 bj-snsetex 35844 wl-equsal1i 36412 mbfresfi 36534 riscer 36856 vvdifopab 37128 opabf 37237 cnvcosseq 37307 antisymressn 37314 trressn 37315 symrelcoss3 37335 cotrintab 42365 pm11.11 43133 fun2dmnopgexmpl 45992 ichv 46117 ichf 46118 ichid 46119 icht 46120 ichcircshi 46122 icheq 46130 mof0ALT 47506 f1omo 47527 |
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