Theorem bj-dfbi4 32558

Description: Alternate definition of the biconditional. (Contributed by BJ, 4-Oct-2019.)

Assertion

Ref	Expression
bj-dfbi4	|- ( ( ph <-> ps ) <-> ( ( ph /\ ps ) \/ -. ( ph \/ ps ) ) )

Proof of Theorem bj-dfbi4

Step	Hyp	Ref	Expression
1		dfbi3 994	. 2 |- ( ( ph <-> ps ) <-> ( ( ph /\ ps ) \/ ( -. ph /\ -. ps ) ) )
2		pm4.56 516	. . 3 |- ( ( -. ph /\ -. ps ) <-> -. ( ph \/ ps ) )
3	2	orbi2i 541	. 2 |- ( ( ( ph /\ ps ) \/ ( -. ph /\ -. ps ) ) <-> ( ( ph /\ ps ) \/ -. ( ph \/ ps ) ) )
4	1, 3	bitri 264	1 |- ( ( ph <-> ps ) <-> ( ( ph /\ ps ) \/ -. ( ph \/ ps ) ) )

Syntax hints:   -. wn 3   <-> 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:  bj-dfbi5  32559