Theorem syl2an2

Description: syl2an with antecedents in standard conjunction form. (Contributed by Alan Sare, 27-Aug-2016)

	Ref	Expression
Hypotheses	syl2an2.1	⊢ ( 𝜑 → 𝜓 )
	syl2an2.2	⊢ ( ( 𝜒 ∧ 𝜑 ) → 𝜃 )
	syl2an2.3	⊢ ( ( 𝜓 ∧ 𝜃 ) → 𝜏 )
Assertion	syl2an2	⊢ ( ( 𝜒 ∧ 𝜑 ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		syl2an2.1	⊢ ( 𝜑 → 𝜓 )
2		syl2an2.2	⊢ ( ( 𝜒 ∧ 𝜑 ) → 𝜃 )
3		syl2an2.3	⊢ ( ( 𝜓 ∧ 𝜃 ) → 𝜏 )
4	1	adantl	⊢ ( ( 𝜒 ∧ 𝜑 ) → 𝜓 )
5	4 2 3	syl2anc	⊢ ( ( 𝜒 ∧ 𝜑 ) → 𝜏 )