Theorem syl2im

Description: Replace two antecedents. Implication-only version of syl2an . (Contributed by Wolf Lammen, 14-May-2013)

	Ref	Expression
Hypotheses	syl2im.1	⊢ ( 𝜑 → 𝜓 )
	syl2im.2	⊢ ( 𝜒 → 𝜃 )
	syl2im.3	⊢ ( 𝜓 → ( 𝜃 → 𝜏 ) )
Assertion	syl2im	⊢ ( 𝜑 → ( 𝜒 → 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		syl2im.1	⊢ ( 𝜑 → 𝜓 )
2		syl2im.2	⊢ ( 𝜒 → 𝜃 )
3		syl2im.3	⊢ ( 𝜓 → ( 𝜃 → 𝜏 ) )
4	2 3	syl5	⊢ ( 𝜓 → ( 𝜒 → 𝜏 ) )
5	1 4	syl	⊢ ( 𝜑 → ( 𝜒 → 𝜏 ) )