Theorem wl-embant 33293

Description: A true wff can always be added as a nested antecedent to an antecedent. Note: this theorem is intuitionistically valid. (Contributed by Wolf Lammen, 4-Oct-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
wl-embant.1	|- ph
wl-embant.2	|- ( ps -> ch )

Assertion

Ref	Expression
wl-embant	|- ( ( ph -> ps ) -> ch )

Proof of Theorem wl-embant

Step	Hyp	Ref	Expression
1		wl-embant.1	. 2 |- ph
2		wl-embant.2	. . 3 |- ( ps -> ch )
3	2	imim2i 16	. 2 |- ( ( ph -> ps ) -> ( ph -> ch ) )
4	1, 3	mpi 20	1 |- ( ( ph -> ps ) -> ch )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by: (None)