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Theorem 3adant3r 1235
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
Hypothesis
Ref Expression
3adant1l.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant3r ((𝜑𝜓 ∧ (𝜒𝜏)) → 𝜃)

Proof of Theorem 3adant3r
StepHypRef Expression
1 3adant1l.1 . . . 4 ((𝜑𝜓𝜒) → 𝜃)
213com13 1208 . . 3 ((𝜒𝜓𝜑) → 𝜃)
323adant1r 1231 . 2 (((𝜒𝜏) ∧ 𝜓𝜑) → 𝜃)
433com13 1208 1 ((𝜑𝜓 ∧ (𝜒𝜏)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  w3a 978
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 980
This theorem is referenced by:  addassnqg  7384  mulassnqg  7386  prarloc  7505  ltpopr  7597  ltexprlemfl  7611  ltexprlemfu  7613  addasssrg  7758  axaddass  7874  apmul1  8748  ltmul2  8816  lemul2  8817  dvdscmulr  11830  dvdsmulcr  11831  modremain  11937  ndvdsadd  11939  rpexp12i  12158  xblcntrps  14053  xblcntr  14054
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