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


Ref 
Expression 

Assertion 
simpr1r 
$${\u22a2}\left({\tau}\wedge \left(\left({\phi}\wedge {\psi}\right)\wedge {\chi}\wedge {\theta}\right)\right)\to {\psi}$$ 
Proof
Step 
Hyp 
Ref 
Expression 
1 

simprr 
$${\u22a2}\left({\tau}\wedge \left({\phi}\wedge {\psi}\right)\right)\to {\psi}$$ 
2 
1

3ad2antr1 
$${\u22a2}\left({\tau}\wedge \left(\left({\phi}\wedge {\psi}\right)\wedge {\chi}\wedge {\theta}\right)\right)\to {\psi}$$ 