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Theorem 3ad2antl2 1144
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)
Hypothesis
Ref Expression
3ad2antl.1 ((𝜑𝜒) → 𝜃)
Assertion
Ref Expression
3ad2antl2 (((𝜓𝜑𝜏) ∧ 𝜒) → 𝜃)

Proof of Theorem 3ad2antl2
StepHypRef Expression
1 3ad2antl.1 . . 3 ((𝜑𝜒) → 𝜃)
21adantlr 468 . 2 (((𝜑𝜏) ∧ 𝜒) → 𝜃)
323adantl1 1137 1 (((𝜓𝜑𝜏) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 962
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 964
This theorem is referenced by:  fcofo  5685  cocan1  5688  acexmid  5773  caovimo  5964  ordiso2  6920  mkvprop  7032  ltpopr  7415  ltsopr  7416  addcanprleml  7434  addcanprlemu  7435  aptiprlemu  7460  muldvds1  11529  lcmdvds  11771  cnpnei  12402
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