Theorem bj-nnclavc 34422

Description: Commuted form of bj-nnclav 34420. Notice the non-intuitionistic proof from bj-peircei 34440 and imim1i 63. (Contributed by BJ, 30-Jul-2024.) A proof which is shorter when compressed uses embantd 59. (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-nnclavc	⊢ ((𝜑 → 𝜓) → (((𝜑 → 𝜓) → 𝜑) → 𝜓))

Proof of Theorem bj-nnclavc

Step	Hyp	Ref	Expression
1		bj-nnclav 34420	. 2 ⊢ (((𝜑 → 𝜓) → 𝜑) → ((𝜑 → 𝜓) → 𝜓))
2	1	com12 32	1 ⊢ ((𝜑 → 𝜓) → (((𝜑 → 𝜓) → 𝜑) → 𝜓))

Syntax hints:   → wi 4

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

This theorem is referenced by:  bj-nnclavci  34423