Theorem uunT21 38030

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 3-Dec-2015.) (Proof modification is discouraged.) (New usage is discouraged.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
uunT21.1	⊢ ((⊤ ∧ (𝜑 ∧ 𝜓)) → 𝜒)

Assertion

Ref	Expression
uunT21	⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Proof of Theorem uunT21

Step	Hyp	Ref	Expression
1		uunT21.1	. 2 ⊢ ((⊤ ∧ (𝜑 ∧ 𝜓)) → 𝜒)
2	1	uunT1 38028	1 ⊢ ((𝜑 ∧ 𝜓) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 383  ⊤wtru 1476

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 196  df-or 384  df-an 385  df-tru 1478

This theorem is referenced by: (None)