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Metamath Proof Explorer

Theorem tbw-ax1

Description: The first of four axioms in the Tarski-Bernays-Wajsberg system. (Contributed by Anthony Hart, 13-Aug-2011) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	tbw-ax1	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜓 → 𝜒 ) → ( 𝜑 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		imim1	⊢ ( ( 𝜑 → 𝜓 ) → ( ( 𝜓 → 𝜒 ) → ( 𝜑 → 𝜒 ) ) )