Theorem anandirs 804

Description: Inference that undistributes conjunction in the antecedent. (Contributed by NM, 7-Jun-2004.)

Hypothesis

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

Assertion

Ref	Expression
anandirs	⊢ (((φ ∧ ψ) ∧ χ) → τ)

Proof of Theorem anandirs

Step	Hyp	Ref	Expression
1		anandirs.1	. . 3 ⊢ (((φ ∧ χ) ∧ (ψ ∧ χ)) → τ)
2	1	an4s 799	. 2 ⊢ (((φ ∧ ψ) ∧ (χ ∧ χ)) → τ)
3	2	anabsan2 795	1 ⊢ (((φ ∧ ψ) ∧ χ) → τ)

This proof depends on syntax axioms:   → wi 4   ∧ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  3impdir  1238  fvreseq  5399