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Theorem syl2imc 40
 Description: A commuted version of syl2im 39. Implication-only version of syl2anr 494. (Contributed by BJ, 20-Oct-2021.)
Hypotheses
Ref Expression
syl2im.1 (𝜑𝜓)
syl2im.2 (𝜒𝜃)
syl2im.3 (𝜓 → (𝜃𝜏))
Assertion
Ref Expression
syl2imc (𝜒 → (𝜑𝜏))

Proof of Theorem syl2imc
StepHypRef Expression
1 syl2im.1 . . 3 (𝜑𝜓)
2 syl2im.2 . . 3 (𝜒𝜃)
3 syl2im.3 . . 3 (𝜓 → (𝜃𝜏))
41, 2, 3syl2im 39 . 2 (𝜑 → (𝜒𝜏))
54com12 32 1 (𝜒 → (𝜑𝜏))
 Colors of variables: wff setvar class Syntax hints:   → wi 4 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7 This theorem is referenced by:  triun  4694  rankpwi  8569  2cshwcshw  13422  incexclem  14407  sumeven  14948  cygth  19739  cnpco  20881  txkgen  21265  sizeusglecusglem1  26012  ontgval  31600  bj-dvelimdv1  32028  iccpartgt  39965  bgoldbtbndlem3  40223  2ffzoeq  40361
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