Theorem bigolden 862

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		pm4.71 369	. 2 |- ( ( ph -> ps ) <-> ( ph <-> ( ph /\ ps ) ) )
2		pm4.72 736	. 2 |- ( ( ph -> ps ) <-> ( ps <-> ( ph \/ ps ) ) )
3		bicom 128	. 2 |- ( ( ph <-> ( ph /\ ps ) ) <-> ( ( ph /\ ps ) <-> ph ) )
4	1, 2, 3	3bitr3ri 200	1 |- ( ( ( ph /\ ps ) <-> ph ) <-> ( ps <-> ( ph \/ ps ) ) )

Syntax hints:   -> wi 4   /\ wa 97   <-> wb 98   \/ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)