Theorem an42s 661

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 660	. 2 ⊢ (((𝜑 ∧ 𝜒) ∧ (𝜓 ∧ 𝜃)) → 𝜏)
3	2	ancom2s 650	1 ⊢ (((𝜑 ∧ 𝜒) ∧ (𝜃 ∧ 𝜓)) → 𝜏)

Syntax hints:   → wi 4   ∧ wa 399

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 210  df-an 400

This theorem is referenced by:  nnmsucr  8353  ecopoveq  8500  sbthlem9  8764  mulclsr  10698  mulasssr  10704  distrsr  10705  ltsosr  10708  axmulf  10760  axmulass  10771  axdistr  10772  subadd4  11122  mulsub  11275  mgmidmo  18132  tgcl  21866  bwth  22307  pntibndlem2  26472  hosubadd4  29895  pibt2  35325  lindsadd  35507  fdc  35640  isdrngo2  35853  unichnidl  35926  acongtr  40503