Theorem anabss7p1 42407

Description: A deduction unionizing a non-unionized collection of virtual hypotheses. This would have been named uun221 if the 0th permutation did not exist in set.mm as anabss7 670. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
anabss7p1.1	⊢ (((𝜓 ∧ 𝜑) ∧ 𝜑) → 𝜒)

Assertion

Ref	Expression
anabss7p1	⊢ ((𝜓 ∧ 𝜑) → 𝜒)

Proof of Theorem anabss7p1

Step	Hyp	Ref	Expression
1		anabss7p1.1	. 2 ⊢ (((𝜓 ∧ 𝜑) ∧ 𝜑) → 𝜒)
2	1	anabss3 672	1 ⊢ ((𝜓 ∧ 𝜑) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 396

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 397

This theorem is referenced by: (None)