Metamath Proof Explorer
Description: Simplification of conjunction. (Contributed by NM, 9Mar2012) (Proof
shortened by Wolf Lammen, 23Jun2022)


Ref 
Expression 

Assertion 
simprl3 
$${\u22a2}\left({\tau}\wedge \left(\left({\phi}\wedge {\psi}\wedge {\chi}\right)\wedge {\theta}\right)\right)\to {\chi}$$ 
Proof
Step 
Hyp 
Ref 
Expression 
1 

simp3 
$${\u22a2}\left({\phi}\wedge {\psi}\wedge {\chi}\right)\to {\chi}$$ 
2 
1

ad2antrl 
$${\u22a2}\left({\tau}\wedge \left(\left({\phi}\wedge {\psi}\wedge {\chi}\right)\wedge {\theta}\right)\right)\to {\chi}$$ 