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  6587  ecopoveq  6730  enqdc  7494  addcmpblnq  7500  addpipqqslem  7502  addpipqqs  7503  addclnq  7508  addcomnqg  7514  distrnqg  7520  recexnq  7523  ltdcnq  7530  ltexnqq  7541  enq0enq  7564  enq0sym  7565  enq0breq  7569  addclnq0  7584  distrnq0  7592  mulclsr  7887  axmulass  8006  axdistr  8007  subadd4  8336  mulsub  8493  mgmidmo  13279  tgcl  14611