Theorem bigolden 901

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		pm4.71 611	. 2 |- ((ph -> ps) <-> (ph <-> (ph /\ ps)))
2		pm4.72 846	. 2 |- ((ph -> ps) <-> (ps <-> (ph \/ ps)))
3		bicom 191	. 2 |- ((ph <-> (ph /\ ps)) <-> ((ph /\ ps) <-> ph))
4	1, 2, 3	3bitr3ri 267	1 |- (((ph /\ ps) <-> ph) <-> (ps <-> (ph \/ ps)))

Syntax hints:   -> wi 4   <-> wb 176   \/ wo 357   /\ 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-or 359  df-an 360

This theorem is referenced by: (None)