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Metamath Proof Explorer

Theorem jccir

Description: Inference conjoining a consequent of a consequent to the right of the consequent in an implication. See also ex-natded5.3i . (Contributed by Mario Carneiro, 9-Feb-2017) (Revised by AV, 20-Aug-2019)

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

Proof

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