Theorem bj-dfbi5 32559

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

Assertion

Ref	Expression
bj-dfbi5	|- ( ( ph <-> ps ) <-> ( ( ph \/ ps ) -> ( ph /\ ps ) ) )

Proof of Theorem bj-dfbi5

Step	Hyp	Ref	Expression
1		orcom 402	. 2 |- ( ( ( ph /\ ps ) \/ -. ( ph \/ ps ) ) <-> ( -. ( ph \/ ps ) \/ ( ph /\ ps ) ) )
2		bj-dfbi4 32558	. 2 |- ( ( ph <-> ps ) <-> ( ( ph /\ ps ) \/ -. ( ph \/ ps ) ) )
3		imor 428	. 2 |- ( ( ( ph \/ ps ) -> ( ph /\ ps ) ) <-> ( -. ( ph \/ ps ) \/ ( ph /\ ps ) ) )
4	1, 2, 3	3bitr4i 292	1 |- ( ( ph <-> ps ) <-> ( ( ph \/ ps ) -> ( ph /\ ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> 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-dfbi6  32560