Theorem anabsi5 790

Description: Absorption of antecedent into conjunction. (Contributed by NM, 11-Jun-1995.) (Proof shortened by Wolf Lammen, 18-Nov-2013.)

Hypothesis

Ref	Expression
anabsi5.1	⊢ (φ → ((φ ∧ ψ) → χ))

Assertion

Ref	Expression
anabsi5	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem anabsi5

Step	Hyp	Ref	Expression
1		anabsi5.1	. . 3 ⊢ (φ → ((φ ∧ ψ) → χ))
2	1	imp 418	. 2 ⊢ ((φ ∧ (φ ∧ ψ)) → χ)
3	2	anabss5 789	1 ⊢ ((φ ∧ ψ) → χ)

Syntax hints:   → wi 4   ∧ wa 358

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 177  df-an 360

This theorem is referenced by:  anabsi6  791  anabsi8  793  3anidm12  1239  rspce  2951