Theorem uun121 45519

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
uun121.1	⊢ ((𝜑 ∧ (𝜑 ∧ 𝜓)) → 𝜒)

Assertion

Ref	Expression
uun121	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem uun121

Step	Hyp	Ref	Expression
1		anabs5 675	. 2 ⊢ ((𝜑 ∧ (𝜑 ∧ 𝜓)) ↔ (𝜑 ∧ 𝜓))
2		uun121.1	. 2 ⊢ ((𝜑 ∧ (𝜑 ∧ 𝜓)) → 𝜒)
3	1, 2	sylbir 238	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

This proof depends on syntax axioms:   → wi 4   ∧ wa 400

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 401

This theorem is used by: (None)