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Theorem 3simpb 913
Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994.)
Assertion
Ref Expression
3simpb ((𝜑𝜓𝜒) → (𝜑𝜒))

Proof of Theorem 3simpb
StepHypRef Expression
1 3ancomb 904 . 2 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
2 3simpa 912 . 2 ((𝜑𝜒𝜓) → (𝜑𝜒))
31, 2sylbi 118 1 ((𝜑𝜓𝜒) → (𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  3adant2  934  3adantl2  1072  3adantr2  1075  enq0tr  6589  ixxssixx  8871  qbtwnzlemshrink  9205  rebtwn2zlemshrink  9209  muldvds1  10131  dvds2add  10140  dvds2sub  10141  dvdstr  10143  pw2dvdslemn  10232
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