Theorem wl-embant 37445

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	⊢ 𝜑
wl-embant.2	⊢ (𝜓 → 𝜒)

Assertion

Ref	Expression
wl-embant	⊢ ((𝜑 → 𝜓) → 𝜒)

Proof of Theorem wl-embant

Step	Hyp	Ref	Expression
1		wl-embant.1	. 2 ⊢ 𝜑
2		wl-embant.2	. . 3 ⊢ (𝜓 → 𝜒)
3	2	imim2i 16	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜒))
4	1, 3	mpi 20	1 ⊢ ((𝜑 → 𝜓) → 𝜒)

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)