Theorem bigolden 747

Description: Dijkstra-Scholten's Golden Rule for calculational proofs.

Assertion

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

Proof of Theorem bigolden

Step	Hyp	Ref	Expression
1		pm4.71 635	. 2 |- ((ph -> ps) <-> (ph <-> (ph /\ ps)))
2		pm4.72 641	. 2 |- ((ph -> ps) <-> (ps <-> (ph \/ ps)))
3		bicom 520	. 2 |- ((ph <-> (ph /\ ps)) <-> ((ph /\ ps) <-> ph))
4	1, 2, 3	3bitr3r 182	1 |- (((ph /\ ps) <-> ph) <-> (ps <-> (ph \/ ps)))

Syntax hints:   -> wi 3   <-> wb 146   \/ wo 222   /\ wa 223

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225

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