Theorem an32 773

Description: A rearrangement of conjuncts. (Contributed by NM, 12-Mar-1995.) (Proof shortened by Wolf Lammen, 25-Dec-2012.)

Assertion

Ref	Expression
an32	|- (((ph /\ ps) /\ ch) <-> ((ph /\ ch) /\ ps))

Proof of Theorem an32

Step	Hyp	Ref	Expression
1		anass 630	. 2 |- (((ph /\ ps) /\ ch) <-> (ph /\ (ps /\ ch)))
2		an12 772	. 2 |- ((ph /\ (ps /\ ch)) <-> (ps /\ (ph /\ ch)))
3		ancom 437	. 2 |- ((ps /\ (ph /\ ch)) <-> ((ph /\ ch) /\ ps))
4	1, 2, 3	3bitri 262	1 |- (((ph /\ ps) /\ ch) <-> ((ph /\ ch) /\ ps))

Syntax hints:   <-> wb 176   /\ wa 358

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 177  df-an 360

This theorem is referenced by:  an32s  779  3anan32  946  indifdir  3512  inrab2  3529  reupick  3540  resco  5086  imadif  5172  dff1o3  5293  f11o  5316  respreima  5411  dff1o6  5476  brpprod  5840