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Metamath Proof Explorer

Theorem jccil

Description: Inference conjoining a consequent of a consequent to the left of the consequent in an implication. Remark: One can also prove this theorem using syl and jca (as done in jccir ), which would be 4 bytes shorter, but one step longer than the current proof. (Proof modification is discouraged.) (Contributed by AV, 20-Aug-2019)

	Ref	Expression
Hypotheses	jccir.1	⊢ ( 𝜑 → 𝜓 )
	jccir.2	⊢ ( 𝜓 → 𝜒 )
Assertion	jccil	⊢ ( 𝜑 → ( 𝜒 ∧ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		jccir.1	⊢ ( 𝜑 → 𝜓 )
2		jccir.2	⊢ ( 𝜓 → 𝜒 )
3	1 2	jccir	⊢ ( 𝜑 → ( 𝜓 ∧ 𝜒 ) )
4	3	ancomd	⊢ ( 𝜑 → ( 𝜒 ∧ 𝜓 ) )