Theorem uun123p4 45553

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
uun123p4.1	⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃)

Assertion

Ref	Expression
uun123p4	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

Proof of Theorem uun123p4

Step	Hyp	Ref	Expression
1		uun123p4.1	. 2 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) → 𝜃)
2	1	3com13 1142	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃)

This proof depends on syntax axioms:   → wi 4   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by: (None)