Theorem uun123p3 42104

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
uun123p3.1	⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜃)

Assertion

Ref	Expression
uun123p3	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Proof of Theorem uun123p3

Step	Hyp	Ref	Expression
1		uun123p3.1	. 2 ⊢ ((𝜓 ∧ 𝜒 ∧ 𝜑) → 𝜃)
2	1	3comr 1127	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Syntax hints:   → wi 4   ∧ w3a 1089

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 210  df-an 400  df-3an 1091

This theorem is referenced by: (None)