Theorem an13 774

Description: A rearrangement of conjuncts. (Contributed by NM, 24-Jun-2012.) (Proof shortened by Wolf Lammen, 31-Dec-2012.)

Assertion

Ref	Expression
an13	|- ((ph /\ (ps /\ ch)) <-> (ch /\ (ps /\ ph)))

Proof of Theorem an13

Step	Hyp	Ref	Expression
1		an12 772	. 2 |- ((ph /\ (ps /\ ch)) <-> (ps /\ (ph /\ ch)))
2		anass 630	. 2 |- (((ps /\ ph) /\ ch) <-> (ps /\ (ph /\ ch)))
3		ancom 437	. 2 |- (((ps /\ ph) /\ ch) <-> (ch /\ (ps /\ ph)))
4	1, 2, 3	3bitr2i 264	1 |- ((ph /\ (ps /\ ch)) <-> (ch /\ (ps /\ ph)))

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:  an31  775  eqvinop  4606  elxp2  4802  iunfopab  5204