Theorem an42s 674

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 673	. 2 ⊢ (((𝜑 ∧ 𝜒) ∧ (𝜓 ∧ 𝜃)) → 𝜏)
3	2	ancom2s 663	1 ⊢ (((𝜑 ∧ 𝜒) ∧ (𝜃 ∧ 𝜓)) → 𝜏)

This proof depends on syntax axioms:   → wi 4   ∧ wa 401

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

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  nnmsucr  8627  ecopoveq  8832  sbthlem9  9107  mulclsr  11162  mulasssr  11168  distrsr  11169  ltsosr  11172  axmulf  11224  axmulass  11235  axdistr  11236  subadd4  11595  mulsub  11752  mgmidmo  18831  isdrng3lem2  20999  tgcl  23280  bwth  23721  pntibndlem2  27911  hosubadd4  32409  pibt2  38320  lindsadd  38516  fdc  38659  isdrngo2  38872  unichnidl  38945  acongtr  43964