Theorem an42s 593

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 592	. 2 ⊢ (((𝜑 ∧ 𝜒) ∧ (𝜓 ∧ 𝜃)) → 𝜏)
3	2	ancom2s 568	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  6656  ecopoveq  6799  enqdc  7581  addcmpblnq  7587  addpipqqslem  7589  addpipqqs  7590  addclnq  7595  addcomnqg  7601  distrnqg  7607  recexnq  7610  ltdcnq  7617  ltexnqq  7628  enq0enq  7651  enq0sym  7652  enq0breq  7656  addclnq0  7671  distrnq0  7679  mulclsr  7974  axmulass  8093  axdistr  8094  subadd4  8423  mulsub  8580  mgmidmo  13460  tgcl  14794