Theorem eelT0

Description: An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	eelT0.1	⊢ ( ⊤ → 𝜑 )
	eelT0.2	⊢ 𝜓
	eelT0.3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
Assertion	eelT0	⊢ 𝜒

Proof

Step	Hyp	Ref	Expression
1		eelT0.1	⊢ ( ⊤ → 𝜑 )
2		eelT0.2	⊢ 𝜓
3		eelT0.3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
4	1 3	sylan	⊢ ( ( ⊤ ∧ 𝜓 ) → 𝜒 )
5	2 4	mpan2	⊢ ( ⊤ → 𝜒 )
6	5	mptru	⊢ 𝜒