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Metamath Proof Explorer

Theorem e1a

Description: A Virtual deduction elimination rule. syl is e1a without virtual deductions. (Contributed by Alan Sare, 11-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e1a.1	⊢ ( 𝜑 ▶ 𝜓 )
	e1a.2	⊢ ( 𝜓 → 𝜒 )
Assertion	e1a	⊢ ( 𝜑 ▶ 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		e1a.1	⊢ ( 𝜑 ▶ 𝜓 )
2		e1a.2	⊢ ( 𝜓 → 𝜒 )
3	1	in1	⊢ ( 𝜑 → 𝜓 )
4	3 2	syl	⊢ ( 𝜑 → 𝜒 )
5	4	dfvd1ir	⊢ ( 𝜑 ▶ 𝜒 )