Theorem an2anr 33998

Description: Double commutation in conjunction. (Contributed by Peter Mazsa, 27-Jun-2019.)

Assertion

Ref	Expression
an2anr	|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ps /\ ph ) /\ ( th /\ ch ) ) )

Proof of Theorem an2anr

Step	Hyp	Ref	Expression
1		ancom 466	. 2 |- ( ( ph /\ ps ) <-> ( ps /\ ph ) )
2		ancom 466	. 2 |- ( ( ch /\ th ) <-> ( th /\ ch ) )
3	1, 2	anbi12i 733	1 |- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ps /\ ph ) /\ ( th /\ ch ) ) )

Syntax hints:   <-> wb 196   /\ 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)