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Metamath Proof Explorer

Theorem ee13

Description: e13 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 28-Oct-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee13.1	⊢ ( 𝜑 → 𝜓 )
	ee13.2	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
	ee13.3	⊢ ( 𝜓 → ( 𝜏 → 𝜂 ) )
Assertion	ee13	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜂 ) ) )

Proof

Step	Hyp	Ref	Expression
1		ee13.1	⊢ ( 𝜑 → 𝜓 )
2		ee13.2	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) )
3		ee13.3	⊢ ( 𝜓 → ( 𝜏 → 𝜂 ) )
4	1 3	syl	⊢ ( 𝜑 → ( 𝜏 → 𝜂 ) )
5	2 4	syl6d	⊢ ( 𝜑 → ( 𝜒 → ( 𝜃 → 𝜂 ) ) )