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Metamath Proof Explorer

Theorem ee3bir

Description: Right-biconditional form of e3 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 22-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee3bir.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
	ee3bir.2	⊢ ( 𝜏 ↔ 𝜃 )
Assertion	ee3bir	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee3bir.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2		ee3bir.2	⊢ ( 𝜏 ↔ 𝜃 )
3	2	biimpri	⊢ ( 𝜃 → 𝜏 )
4	1 3	syl8	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜏 ) ) )