Theorem syl2imc

Description: A commuted version of syl2im . Implication-only version of syl2anr . (Contributed by BJ, 20-Oct-2021)

	Ref	Expression
Hypotheses	syl2im.1	⊢ ( 𝜑 → 𝜓 )
	syl2im.2	⊢ ( 𝜒 → 𝜃 )
	syl2im.3	⊢ ( 𝜓 → ( 𝜃 → 𝜏 ) )
Assertion	syl2imc	⊢ ( 𝜒 → ( 𝜑 → 𝜏 ) )

Proof

Step	Hyp	Ref	Expression
1		syl2im.1	⊢ ( 𝜑 → 𝜓 )
2		syl2im.2	⊢ ( 𝜒 → 𝜃 )
3		syl2im.3	⊢ ( 𝜓 → ( 𝜃 → 𝜏 ) )
4	1 2 3	syl2im	⊢ ( 𝜑 → ( 𝜒 → 𝜏 ) )
5	4	com12	⊢ ( 𝜒 → ( 𝜑 → 𝜏 ) )