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Theorem 3simpb 937
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 928 . 2 ((𝜑𝜓𝜒) ↔ (𝜑𝜒𝜓))
2 3simpa 936 . 2 ((𝜑𝜒𝜓) → (𝜑𝜒))
31, 2sylbi 119 1 ((𝜑𝜓𝜒) → (𝜑𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 920
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  df-3an 922
This theorem is referenced by:  3adant2  958  3adantl2  1096  3adantr2  1099  enq0tr  6896  ixxssixx  9215  rebtwn2zlemshrink  9554  muldvds1  10601  dvds2add  10610  dvds2sub  10611  dvdstr  10613  pw2dvdslemn  10923
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