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Metamath Proof Explorer

Theorem int2

Description: The virtual deduction introduction rule of converting the end virtual hypothesis of 2 virtual hypotheses into an antecedent. Conventional form of int2 is ex . (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	int2.1	⊢ ( ( 𝜑 , 𝜓 ) ▶ 𝜒 )
	Assertion	int2	⊢ ( 𝜑 ▶ ( 𝜓 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		int2.1	⊢ ( ( 𝜑 , 𝜓 ) ▶ 𝜒 )
2	1	dfvd2ani	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
3	2	ex	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4	3	dfvd1ir	⊢ ( 𝜑 ▶ ( 𝜓 → 𝜒 ) )