Theorem mpd3an3

Description: An inference based on modus ponens. (Contributed by NM, 8-Nov-2007)

	Ref	Expression
Hypotheses	mpd3an3.2	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
	mpd3an3.3	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	mpd3an3	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		mpd3an3.2	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
2		mpd3an3.3	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
3	2	3expa	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) → 𝜃 )
4	1 3	mpdan	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜃 )