Theorem bigolden 945

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		pm4.71 387	. 2 |- ( ( ph -> ps ) <-> ( ph <-> ( ph /\ ps ) ) )
2		pm4.72 817	. 2 |- ( ( ph -> ps ) <-> ( ps <-> ( ph \/ ps ) ) )
3		bicom 139	. 2 |- ( ( ph <-> ( ph /\ ps ) ) <-> ( ( ph /\ ps ) <-> ph ) )
4	1, 2, 3	3bitr3ri 210	1 |- ( ( ( ph /\ ps ) <-> ph ) <-> ( ps <-> ( ph \/ ps ) ) )

Syntax hints:   -> wi 4   /\ wa 103   <-> wb 104   \/ wo 698

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)