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Metamath Proof Explorer

Theorem jctl

Description: Inference conjoining a theorem to the left of a consequent. (Contributed by NM, 31-Dec-1993) (Proof shortened by Wolf Lammen, 24-Oct-2012)

		Ref	Expression
	Hypothesis	jctl.1	⊢ 𝜓
	Assertion	jctl	⊢ ( 𝜑 → ( 𝜓 ∧ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		jctl.1	⊢ 𝜓
2		id	⊢ ( 𝜑 → 𝜑 )
3	2 1	jctil	⊢ ( 𝜑 → ( 𝜓 ∧ 𝜑 ) )