Theorem 3anidm12p2 42316

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.)

Hypothesis

Ref	Expression
3anidm12p2.1	⊢ ((𝜓 ∧ 𝜑 ∧ 𝜑) → 𝜒)

Assertion

Ref	Expression
3anidm12p2	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem 3anidm12p2

Step	Hyp	Ref	Expression
1		3anrot 1098	. . 3 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜑) ↔ (𝜑 ∧ 𝜑 ∧ 𝜓))
2		3anidm12p2.1	. . 3 ⊢ ((𝜓 ∧ 𝜑 ∧ 𝜑) → 𝜒)
3	1, 2	sylbir 234	. 2 ⊢ ((𝜑 ∧ 𝜑 ∧ 𝜓) → 𝜒)
4	3	3anidm12 1417	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1085

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 396  df-3an 1087

This theorem is referenced by: (None)