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Metamath Proof Explorer

Theorem uun121

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	uun121.1	⊢ ( ( 𝜑 ∧ ( 𝜑 ∧ 𝜓 ) ) → 𝜒 )
	Assertion	uun121	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		uun121.1	⊢ ( ( 𝜑 ∧ ( 𝜑 ∧ 𝜓 ) ) → 𝜒 )
2		anabs5	⊢ ( ( 𝜑 ∧ ( 𝜑 ∧ 𝜓 ) ) ↔ ( 𝜑 ∧ 𝜓 ) )
3	2 1	sylbir	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )