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Theorem an32s 535
Description: Swap two conjuncts in antecedent. (Contributed by NM, 13-Mar-1996.)
Hypothesis
Ref Expression
an32s.1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
an32s (((𝜑𝜒) ∧ 𝜓) → 𝜃)

Proof of Theorem an32s
StepHypRef Expression
1 an32 529 . 2 (((𝜑𝜒) ∧ 𝜓) ↔ ((𝜑𝜓) ∧ 𝜒))
2 an32s.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylbi 119 1 (((𝜑𝜒) ∧ 𝜓) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  anass1rs  538  anabss1  543  fssres  5186  foco  5243  fun11iun  5274  fconstfvm  5515  isocnv  5590  f1oiso  5605  f1ocnvfv3  5641  tfrcl  6129  mapxpen  6564  findcard  6604  exmidfodomrlemim  6827  genpassl  7083  genpassu  7084  cnegexlem3  7659  recexaplem2  8121  divap0  8151  dfinfre  8417  qreccl  9127  xrlttr  9265  addmodlteq  9805  cau3lem  10547  climcn1  10697  climcn2  10698  climcaucn  10740  rplpwr  11294  dvdssq  11298  nn0seqcvgd  11301  lcmgcdlem  11337  isprm6  11404  phiprmpw  11476  cncfco  11647
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