Metamath Proof Explorer
Description: Simplification of conjunction. (Contributed by NM, 9Mar2012) (Proof
shortened by Wolf Lammen, 24Jun2022)


Ref 
Expression 

Assertion 
simpl13 
$${\u22a2}\left(\left(\left({\phi}\wedge {\psi}\wedge {\chi}\right)\wedge {\theta}\wedge {\tau}\right)\wedge {\eta}\right)\to {\chi}$$ 
Proof
Step 
Hyp 
Ref 
Expression 
1 

simpl3 
$${\u22a2}\left(\left({\phi}\wedge {\psi}\wedge {\chi}\right)\wedge {\eta}\right)\to {\chi}$$ 
2 
1

3ad2antl1 
$${\u22a2}\left(\left(\left({\phi}\wedge {\psi}\wedge {\chi}\right)\wedge {\theta}\wedge {\tau}\right)\wedge {\eta}\right)\to {\chi}$$ 