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Metamath Proof Explorer

Theorem exbiri

Description: Inference form of exbir . This proof is exbiriVD automatically translated and minimized. (Contributed by Alan Sare, 31-Dec-2011) (Proof shortened by Wolf Lammen, 27-Jan-2013)

		Ref	Expression
	Hypothesis	exbiri.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ↔ 𝜃 ) )
	Assertion	exbiri	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		exbiri.1	⊢ ( ( 𝜑 ∧ 𝜓 ) → ( 𝜒 ↔ 𝜃 ) )
2	1	biimpar	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜃 ) → 𝜒 )
3	2	exp31	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → 𝜒 ) ) )