Theorem ifpnot

Description: Restate negated wff as conditional logic operator. (Contributed by RP, 20-Apr-2020)

	Ref	Expression
Assertion	ifpnot	|- ( -. ph <-> if- ( ph , F. , T. ) )

Proof

Step	Hyp	Ref	Expression
1		tru	|- T.
2	1	olci	|- ( ph \/ T. )
3	2	biantru	|- ( ( -. ph \/ F. ) <-> ( ( -. ph \/ F. ) /\ ( ph \/ T. ) ) )
4		fal	|- -. F.
5	4	biorfri	|- ( -. ph <-> ( -. ph \/ F. ) )
6		dfifp4	|- ( if- ( ph , F. , T. ) <-> ( ( -. ph \/ F. ) /\ ( ph \/ T. ) ) )
7	3 5 6	3bitr4i	|- ( -. ph <-> if- ( ph , F. , T. ) )