Theorem uun121 42292

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 659	. 2 ⊢ ((𝜑 ∧ (𝜑 ∧ 𝜓)) ↔ (𝜑 ∧ 𝜓))
2		uun121.1	. 2 ⊢ ((𝜑 ∧ (𝜑 ∧ 𝜓)) → 𝜒)
3	1, 2	sylbir 234	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 395

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

This theorem is referenced by: (None)