Theorem bigolden 976

Description: Dijkstra-Scholten's Golden Rule for calculational proofs. (Contributed by NM, 10-Jan-2005.)

Assertion

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

Proof of Theorem bigolden

Step	Hyp	Ref	Expression
1		pm4.71 662	. 2 |- ( ( ph -> ps ) <-> ( ph <-> ( ph /\ ps ) ) )
2		pm4.72 920	. 2 |- ( ( ph -> ps ) <-> ( ps <-> ( ph \/ ps ) ) )
3		bicom 212	. 2 |- ( ( ph <-> ( ph /\ ps ) ) <-> ( ( ph /\ ps ) <-> ph ) )
4	1, 2, 3	3bitr3ri 291	1 |- ( ( ( ph /\ ps ) <-> ph ) <-> ( ps <-> ( ph \/ ps ) ) )

Syntax hints:   -> wi 4   <-> wb 196   \/ wo 383   /\ 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-or 385  df-an 386

This theorem is referenced by: (None)