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Metamath Proof Explorer

Theorem e2bir

Description: Right biconditional form of e2 . imbitrrdi is e2bir without virtual deductions. (Contributed by Alan Sare, 29-Apr-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e2bir.1	⊢ ( 𝜑 , 𝜓 ▶ 𝜒 )
	e2bir.2	⊢ ( 𝜃 ↔ 𝜒 )
Assertion	e2bir	⊢ ( 𝜑 , 𝜓 ▶ 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		e2bir.1	⊢ ( 𝜑 , 𝜓 ▶ 𝜒 )
2		e2bir.2	⊢ ( 𝜃 ↔ 𝜒 )
3	2	biimpri	⊢ ( 𝜒 → 𝜃 )
4	1 3	e2	⊢ ( 𝜑 , 𝜓 ▶ 𝜃 )