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Theorem 3ad2antl3 1108
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)
Hypothesis
Ref Expression
3ad2antl.1 ((𝜑𝜒) → 𝜃)
Assertion
Ref Expression
3ad2antl3 (((𝜓𝜏𝜑) ∧ 𝜒) → 𝜃)

Proof of Theorem 3ad2antl3
StepHypRef Expression
1 3ad2antl.1 . . 3 ((𝜑𝜒) → 𝜃)
21adantll 461 . 2 (((𝜏𝜑) ∧ 𝜒) → 𝜃)
323adantl1 1100 1 (((𝜓𝜏𝜑) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 925
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 927
This theorem is referenced by:  rspc3ev  2739  brcogw  4618  cocan1  5580  ov6g  5796  prarloclemarch2  7039  ltpopr  7215  ltsopr  7216  zdivmul  8897  lcmdvds  11400
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