Theorem clifte 41102

Description: show d is the same as an if-else involving a,b. (Contributed by Jarvin Udandy, 20-Sep-2020.)

Hypotheses

Ref	Expression
clifte.1	|- ( ph /\ -. ch )
clifte.2	|- th

Assertion

Ref	Expression
clifte	|- ( th <-> ( ( ph /\ -. ch ) \/ ( ps /\ ch ) ) )

Proof of Theorem clifte

Step	Hyp	Ref	Expression
1		clifte.2	. 2 |- th
2		clifte.1	. . 3 |- ( ph /\ -. ch )
3	2	orci 405	. 2 |- ( ( ph /\ -. ch ) \/ ( ps /\ ch ) )
4	1, 3	2th 254	1 |- ( th <-> ( ( ph /\ -. ch ) \/ ( ps /\ ch ) ) )

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

This theorem is referenced by: (None)