Theorem anandis 803

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

Hypothesis

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

Assertion

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

Proof of Theorem anandis

Step	Hyp	Ref	Expression
1		anandis.1	. . 3 ⊢ (((φ ∧ ψ) ∧ (φ ∧ χ)) → τ)
2	1	an4s 799	. 2 ⊢ (((φ ∧ φ) ∧ (ψ ∧ χ)) → τ)
3	2	anabsan 786	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:  3impdi  1237  dff13  5472  isotr  5496  f1oiso  5500