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Theorem 3adantl3 1101
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
Hypothesis
Ref Expression
3adantl.1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
3adantl3 (((𝜑𝜓𝜏) ∧ 𝜒) → 𝜃)

Proof of Theorem 3adantl3
StepHypRef Expression
1 3simpa 940 . 2 ((𝜑𝜓𝜏) → (𝜑𝜓))
2 3adantl.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylan 277 1 (((𝜑𝜓𝜏) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 924
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 926
This theorem is referenced by:  ltsopr  7153  lediv2a  8354  muldvds1  11095  muldvds2  11096  dvdscmul  11097  dvdsmulc  11098  rpexp  11406
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