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Metamath Proof Explorer

Theorem el1

Description: A Virtual deduction elimination rule. syl is el1 without virtual deductions. (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	el1.1	⊢ ( 𝜑 ▶ 𝜓 )
	el1.2	⊢ ( 𝜓 → 𝜒 )
Assertion	el1	⊢ ( 𝜑 ▶ 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		el1.1	⊢ ( 𝜑 ▶ 𝜓 )
2		el1.2	⊢ ( 𝜓 → 𝜒 )
3	1	in1	⊢ ( 𝜑 → 𝜓 )
4	3 2	syl	⊢ ( 𝜑 → 𝜒 )
5	4	dfvd1ir	⊢ ( 𝜑 ▶ 𝜒 )