Theorem and_updl ≪ | index | src | ≫

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theorem and_updl (A B C: wff): $ A \and B \imp (A \imp C) \imp C \and B $;

Step	Hyp	Ref	Expression
1		imp_imp_swapl	((A \imp C) \imp A \and B \imp C \and B) \imp A \and B \imp (A \imp C) \imp C \and B
2		imp_intror_and	(A \imp C) \imp A \and B \imp C \and B
3	1, 2	ax_mp	A \and B \imp (A \imp C) \imp C \and B

Axiom use

Logic (ax_mp, ax_1, ax_2, ax_3)