Theorem eelTT

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

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

Proof

Step	Hyp	Ref	Expression
1		eelTT.1	⊢ ( ⊤ → 𝜑 )
2		eelTT.2	⊢ ( ⊤ → 𝜓 )
3		eelTT.3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
4		truan	⊢ ( ( ⊤ ∧ 𝜓 ) ↔ 𝜓 )
5	1 3	sylan	⊢ ( ( ⊤ ∧ 𝜓 ) → 𝜒 )
6	4 5	sylbir	⊢ ( 𝜓 → 𝜒 )
7	2 6	syl	⊢ ( ⊤ → 𝜒 )
8	7	mptru	⊢ 𝜒