Theorem mp3an2ani

Description: An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017)

	Ref	Expression
Hypotheses	mp3an2ani.1	⊢ 𝜑
	mp3an2ani.2	⊢ ( 𝜓 → 𝜒 )
	mp3an2ani.3	⊢ ( ( 𝜓 ∧ 𝜃 ) → 𝜏 )
	mp3an2ani.4	⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜏 ) → 𝜂 )
Assertion	mp3an2ani	⊢ ( ( 𝜓 ∧ 𝜃 ) → 𝜂 )

Proof

Step	Hyp	Ref	Expression
1		mp3an2ani.1	⊢ 𝜑
2		mp3an2ani.2	⊢ ( 𝜓 → 𝜒 )
3		mp3an2ani.3	⊢ ( ( 𝜓 ∧ 𝜃 ) → 𝜏 )
4		mp3an2ani.4	⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜏 ) → 𝜂 )
5	1 2 3 4	mp3an3an	⊢ ( ( 𝜓 ∧ ( 𝜓 ∧ 𝜃 ) ) → 𝜂 )
6	5	anabss5	⊢ ( ( 𝜓 ∧ 𝜃 ) → 𝜂 )