Theorem 3anidm13 1240

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

Hypothesis

Ref	Expression
3anidm13.1	⊢ ((φ ∧ ψ ∧ φ) → χ)

Assertion

Ref	Expression
3anidm13	⊢ ((φ ∧ ψ) → χ)

Proof of Theorem 3anidm13

Step	Hyp	Ref	Expression
1		3anidm13.1	. . 3 ⊢ ((φ ∧ ψ ∧ φ) → χ)
2	1	3com23 1157	. 2 ⊢ ((φ ∧ φ ∧ ψ) → χ)
3	2	3anidm12 1239	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:  ltfinasym  4461  lenltfin  4470