Theorem an42s 800

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

Hypothesis

Ref	Expression
an41r3s.1	⊢ (((φ ∧ ψ) ∧ (χ ∧ θ)) → τ)

Assertion

Ref	Expression
an42s	⊢ (((φ ∧ χ) ∧ (θ ∧ ψ)) → τ)

Proof of Theorem an42s

Step	Hyp	Ref	Expression
1		an41r3s.1	. . 3 ⊢ (((φ ∧ ψ) ∧ (χ ∧ θ)) → τ)
2	1	an4s 799	. 2 ⊢ (((φ ∧ χ) ∧ (ψ ∧ θ)) → τ)
3	2	ancom2s 777	1 ⊢ (((φ ∧ χ) ∧ (θ ∧ ψ)) → 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: (None)