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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)

Colors of variables: wff setvar class

Syntax hints: → wi 4 ∧ wa 358

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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