Theorem retbwax3

Description: tbw-ax3 rederived from merco1 . (Contributed by Anthony Hart, 17-Sep-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	retbwax3	⊢ ( ( ( 𝜑 → 𝜓 ) → 𝜑 ) → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		retbwax2	⊢ ( 𝜑 → ( 𝜑 → 𝜑 ) )
2		merco1lem7	⊢ ( ( 𝜑 → ( 𝜑 → 𝜑 ) ) → ( ( ( 𝜑 → 𝜓 ) → 𝜑 ) → 𝜑 ) )
3	1 2	ax-mp	⊢ ( ( ( 𝜑 → 𝜓 ) → 𝜑 ) → 𝜑 )