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Theorem 3adantr1 1170
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
Hypothesis
Ref Expression
3adantr.1 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
Assertion
Ref Expression
3adantr1 ((𝜑 ∧ (𝜏𝜓𝜒)) → 𝜃)

Proof of Theorem 3adantr1
StepHypRef Expression
1 3simpc 1151 . 2 ((𝜏𝜓𝜒) → (𝜓𝜒))
2 3adantr.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylan2 594 1 ((𝜑 ∧ (𝜏𝜓𝜒)) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  w3a 1088
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 206  df-an 398  df-3an 1090
This theorem is referenced by:  3adant3r1  1183  3ad2antr3  1191  swopo  5560  omeulem1  8533  divmuldiv  11863  imasmnd2  18601  imasgrp2  18870  srgbinomlem2  19966  imasring  20053  abvdiv  20339  mdetunilem9  21992  lly1stc  22870  icccvx  24336  dchrpt  26638  dipsubdir  29839  poimirlem4  36132  fdc  36254  unichnidl  36540  dmncan1  36585  pexmidlem6N  38488  erngdvlem3  39503  erngdvlem3-rN  39511  dvalveclem  39538  dvhvaddass  39610  dvhlveclem  39621  issmflem  45058  prproropf1olem3  45787
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