Theorem prvlem1

Description: An elementary property of the provability predicate. (Contributed by BJ, 3-Apr-2019)

	Ref	Expression
Hypothesis	prvlem1.1	|- ( ph -> ps )
Assertion	prvlem1	|- ( Prv ph -> Prv ps )

Proof

Step	Hyp	Ref	Expression
1		prvlem1.1	|- ( ph -> ps )
2	1	ax-prv1	|- Prv ( ph -> ps )
3		ax-prv2	|- ( Prv ( ph -> ps ) -> ( Prv ph -> Prv ps ) )
4	2 3	ax-mp	|- ( Prv ph -> Prv ps )