Theorem 3anrev 990

Description: Reversal law for triple conjunction. (Contributed by NM, 21-Apr-1994.)

Assertion

Ref	Expression
3anrev	|- ( ( ph /\ ps /\ ch ) <-> ( ch /\ ps /\ ph ) )

Proof of Theorem 3anrev

Step	Hyp	Ref	Expression
1		3ancoma 987	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ph /\ ch ) )
2		3anrot 985	. 2 |- ( ( ch /\ ps /\ ph ) <-> ( ps /\ ph /\ ch ) )
3	1, 2	bitr4i 187	1 |- ( ( ph /\ ps /\ ch ) <-> ( ch /\ ps /\ ph ) )

Syntax hints:   <-> wb 105   /\ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by:  3com13  1210  nnmcan  6586