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Metamath Proof Explorer

Theorem eel0321old

Description: el0321old without virtual deductions. (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	eel0321old.1	⊢ 𝜑
	eel0321old.2	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 )
	eel0321old.3	⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 )
Assertion	eel0321old	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜂 )

Proof

Step	Hyp	Ref	Expression
1		eel0321old.1	⊢ 𝜑
2		eel0321old.2	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 )
3		eel0321old.3	⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 )
4	1 2 3	sylancr	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜂 )