Theorem an42s 589

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 588	. 2 ⊢ (((𝜑 ∧ 𝜒) ∧ (𝜓 ∧ 𝜃)) → 𝜏)
3	2	ancom2s 566	1 ⊢ (((𝜑 ∧ 𝜒) ∧ (𝜃 ∧ 𝜓)) → 𝜏)

Syntax hints:   → wi 4   ∧ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  nnmsucr  6555  ecopoveq  6698  enqdc  7445  addcmpblnq  7451  addpipqqslem  7453  addpipqqs  7454  addclnq  7459  addcomnqg  7465  distrnqg  7471  recexnq  7474  ltdcnq  7481  ltexnqq  7492  enq0enq  7515  enq0sym  7516  enq0breq  7520  addclnq0  7535  distrnq0  7543  mulclsr  7838  axmulass  7957  axdistr  7958  subadd4  8287  mulsub  8444  mgmidmo  13074  tgcl  14384