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Theorem 3adantl1 1071
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
Hypothesis
Ref Expression
3adantl.1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
3adantl1 (((𝜏𝜑𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem 3adantl1
StepHypRef Expression
1 3simpc 914 . 2 ((𝜏𝜑𝜓) → (𝜑𝜓))
2 3adantl.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylan 271 1 (((𝜏𝜑𝜓) ∧ 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:  3ad2antl2  1078  3ad2antl3  1079  distrlem1prl  6737  distrlem1pru  6738  divmuldivap  7762  modqaddmulmod  9335  expnlbnd  9534
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