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Theorem 3adant3r1 1214
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008.)
Hypothesis
Ref Expression
3exp.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant3r1 ((𝜑 ∧ (𝜏𝜓𝜒)) → 𝜃)

Proof of Theorem 3adant3r1
StepHypRef Expression
1 3exp.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213expb 1206 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
323adantr1 1158 1 ((𝜑 ∧ (𝜏𝜓𝜒)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  w3a 980
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 982
This theorem is referenced by:  grpsubsub  13005  grpnnncan2  13013  imasgrp2  13024  mulgnn0ass  13070  mulgsubdir  13074  cmn32  13210  ablsubadd  13218  imasrng  13277  imasring  13381  opprrng  13394  opprring  13396  xmettri3  14277  mettri3  14278  xmetrtri  14279  rprelogbmulexp  14777
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