Theorem an4s 799

Description: Inference rearranging 4 conjuncts in antecedent. (Contributed by NM, 10-Aug-1995.)

Hypothesis

Ref	Expression
an4s.1	⊢ (((φ ∧ ψ) ∧ (χ ∧ θ)) → τ)

Assertion

Ref	Expression
an4s	⊢ (((φ ∧ χ) ∧ (ψ ∧ θ)) → τ)

Proof of Theorem an4s

Step	Hyp	Ref	Expression
1		an4 797	. 2 ⊢ (((φ ∧ χ) ∧ (ψ ∧ θ)) ↔ ((φ ∧ ψ) ∧ (χ ∧ θ)))
2		an4s.1	. 2 ⊢ (((φ ∧ ψ) ∧ (χ ∧ θ)) → τ)
3	1, 2	sylbi 187	1 ⊢ (((φ ∧ χ) ∧ (ψ ∧ θ)) → τ)

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:  an42s  800  anandis  803  anandirs  804  2mo  2282  fnun  5189  f1co  5264  f1oun  5304  f1oco  5308  fntxp  5804  fnpprod  5843  f1opprod  5844  enprmaplem3  6078  sbthlem3  6205  fnfrec  6320