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 ∧ 𝜑 ∧ 𝜑 ) → 𝜒 )
Assertion	3anidm12p2	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		3anidm12p2.1	⊢ ( ( 𝜓 ∧ 𝜑 ∧ 𝜑 ) → 𝜒 )
2		3anrot	⊢ ( ( 𝜓 ∧ 𝜑 ∧ 𝜑 ) ↔ ( 𝜑 ∧ 𝜑 ∧ 𝜓 ) )
3	2 1	sylbir	⊢ ( ( 𝜑 ∧ 𝜑 ∧ 𝜓 ) → 𝜒 )
4	3	3anidm12	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )