Theorem uun123 42317

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
uun123.1	⊢ ((𝜑 ∧ 𝜒 ∧ 𝜓) → 𝜃)

Assertion

Ref	Expression
uun123	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Proof of Theorem uun123

Step	Hyp	Ref	Expression
1		3ancomb 1097	. 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜓) ↔ (𝜑 ∧ 𝜓 ∧ 𝜒))
2		uun123.1	. 2 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜓) → 𝜃)
3	1, 2	sylbir 234	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ 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)