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Theorem 3ad2antl2 1102
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 461 . 2 (((𝜑𝜏) ∧ 𝜒) → 𝜃)
323adantl1 1095 1 (((𝜓𝜑𝜏) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by:  fcofo  5503  cocan1  5506  acexmid  5590  caovimo  5773  ordiso2  6635  ltpopr  7057  ltsopr  7058  addcanprleml  7076  addcanprlemu  7077  aptiprlemu  7102  muldvds1  10601  lcmdvds  10841
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