Metamath Proof Explorer

Theorem bnj253

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

		Ref	Expression
	Assertion	bnj253	\|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps ) /\ ch /\ th ) )

Step	Hyp	Ref	Expression
1		bnj248	\|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ( ph /\ ps ) /\ ch ) /\ th ) )
2		df-3an	\|- ( ( ( ph /\ ps ) /\ ch /\ th ) <-> ( ( ( ph /\ ps ) /\ ch ) /\ th ) )
3	1 2	bitr4i	\|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps ) /\ ch /\ th ) )

Step

Hyp

Ref

Expression

 |-  ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ( ph /\ ps ) /\ ch ) /\ th ) )

 |-  ( ( ( ph /\ ps ) /\ ch /\ th ) <-> ( ( ( ph /\ ps ) /\ ch ) /\ th ) )

1 2

 |-  ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps ) /\ ch /\ th ) )