Metamath Proof Explorer

Theorem 3anidm12p2

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	3anidm12p2.1	$⊢ (ψ \land φ \land φ) \to χ$
	Assertion	3anidm12p2	$⊢ (φ \land ψ) \to χ$

Proof

Step	Hyp	Ref	Expression
1		3anidm12p2.1	$⊢ (ψ \land φ \land φ) \to χ$
2		3anrot	$⊢ (ψ \land φ \land φ) \leftrightarrow (φ \land φ \land ψ)$
3	2 1	sylbir	$⊢ (φ \land φ \land ψ) \to χ$
4	3	3anidm12	$⊢ (φ \land ψ) \to χ$