Theorem 3anidm12 1239

Description: Inference from idempotent law for conjunction. (Contributed by NM, 7-Mar-2008.)

Hypothesis

Ref	Expression
3anidm12.1	⊢ ((φ ∧ φ ∧ ψ) → χ)

Assertion

Ref	Expression
3anidm12	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem 3anidm12

Step	Hyp	Ref	Expression
1		3anidm12.1	. . 3 ⊢ ((φ ∧ φ ∧ ψ) → χ)
2	1	3expib 1154	. 2 ⊢ (φ → ((φ ∧ ψ) → χ))
3	2	anabsi5 790	1 ⊢ ((φ ∧ ψ) → χ)

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

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  df-3an 936

This theorem is referenced by:  3anidm13  1240  dedth3v  3709  eventfin  4518  oddtfin  4519