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Theorem 3adant3r3 1216
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 18-Feb-2008.)
Hypothesis
Ref Expression
3exp.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant3r3 ((𝜑 ∧ (𝜓𝜒𝜏)) → 𝜃)

Proof of Theorem 3adant3r3
StepHypRef Expression
1 3exp.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213expb 1206 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
323adantr3 1160 1 ((𝜑 ∧ (𝜓𝜒𝜏)) → 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:  grpaddsubass  13006  grpsubsub4  13009  grpnpncan  13011  imasgrp2  13024  imasgrp  13025  cmn12  13212  abladdsub  13221  imasrng  13277  imasring  13381  opprrng  13394  opprring  13396  dvrass  13456  lss1  13645  mettri2  14265  xmetrtri  14279
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