Theorem an12i 33900

Description: An inference from commuting operands in a chain of conjunctions. (Contributed by Giovanni Mascellani, 22-May-2019.)

Hypothesis

Ref	Expression
an12i.1	|- ( ph /\ ( ps /\ ch ) )

Assertion

Ref	Expression
an12i	|- ( ps /\ ( ph /\ ch ) )

Proof of Theorem an12i

Step	Hyp	Ref	Expression
1		an12i.1	. 2 |- ( ph /\ ( ps /\ ch ) )
2		an12 838	. 2 |- ( ( ps /\ ( ph /\ ch ) ) <-> ( ph /\ ( ps /\ ch ) ) )
3	1, 2	mpbir 221	1 |- ( ps /\ ( ph /\ ch ) )

Syntax hints:   /\ wa 384

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 197  df-an 386

This theorem is referenced by: (None)