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Metamath Proof Explorer

Theorem ee01an

Description: e01an without virtual deductions. sylancr is also a form of e01an without virtual deduction, except the order of the hypotheses is different. (Contributed by Alan Sare, 25-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee01an.1	⊢ 𝜑
	ee01an.2	⊢ ( 𝜓 → 𝜒 )
	ee01an.3	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )
Assertion	ee01an	⊢ ( 𝜓 → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		ee01an.1	⊢ 𝜑
2		ee01an.2	⊢ ( 𝜓 → 𝜒 )
3		ee01an.3	⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )
4	1 2 3	sylancr	⊢ ( 𝜓 → 𝜃 )