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Mirrors > Home > MPE Home > Th. List > simp-5r | Structured version Visualization version GIF version |
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.) |
Ref | Expression |
---|---|
simp-5r | ⊢ ((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp-4r 803 | . 2 ⊢ (((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜓) | |
2 | 1 | adantr 480 | 1 ⊢ ((((((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜃) ∧ 𝜏) ∧ 𝜂) → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-an 385 |
This theorem is referenced by: simp-6r 807 catcocl 16169 catass 16170 monpropd 16220 subccocl 16328 funcco 16354 funcpropd 16383 mhmmnd 17360 pm2mpmhmlem2 20443 neitr 20794 restutopopn 21852 ustuqtop4 21858 utopreg 21866 cfilucfil 22174 psmetutop 22182 dyadmax 23172 tgifscgr 25203 tgcgrxfr 25213 tgbtwnconn1lem3 25269 tgbtwnconn1 25270 legov 25280 legtrd 25284 legso 25294 miriso 25365 perpneq 25409 footex 25413 colperpex 25425 opphllem 25427 midex 25429 opphl 25446 lnopp2hpgb 25455 trgcopyeu 25498 dfcgra2 25521 inaghl 25531 f1otrg 25551 pthdepisspth 26104 clwlkfclwwlk 26371 2sqmo 28980 omndmul2 29043 psgnfzto1stlem 29181 qtophaus 29231 locfinreflem 29235 cmpcref 29245 pstmxmet 29268 lmxrge0 29326 esumcst 29452 omssubadd 29689 signstfvneq0 29975 afsval 30002 matunitlindflem1 32575 heicant 32614 sstotbnd2 32743 eldioph2b 36344 diophren 36395 pell1234qrdich 36443 iunconlem2 38193 limcrecl 38696 limclner 38718 icccncfext 38773 ioodvbdlimc1lem2 38822 ioodvbdlimc2lem 38824 stoweidlem60 38953 fourierdlem51 39050 fourierdlem77 39076 fourierdlem103 39102 fourierdlem104 39103 smfaddlem1 39649 smfmullem3 39678 clwlksfclwwlk 41269 |
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