Theorem syldc

Description: Syllogism deduction. Commuted form of syld . (Contributed by BJ, 25-Oct-2021)

	Ref	Expression
Hypotheses	syld.1	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
	syld.2	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
Assertion	syldc	⊢ ( 𝜓 → ( 𝜑 → 𝜃 ) )

Proof

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