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Theorem 3ad2antl3 1079
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 453 . 2 (((𝜏𝜑) ∧ 𝜒) → 𝜃)
323adantl1 1071 1 (((𝜓𝜏𝜑) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  w3a 896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114  df-3an 898
This theorem is referenced by:  rspc3ev  2689  brcogw  4532  cocan1  5455  ov6g  5666  prarloclemarch2  6575  ltpopr  6751  ltsopr  6752  zdivmul  8388
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