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Theorem 3adantl2 1103
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
Hypothesis
Ref Expression
3adantl.1 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
3adantl2 (((𝜑𝜏𝜓) ∧ 𝜒) → 𝜃)

Proof of Theorem 3adantl2
StepHypRef Expression
1 3simpb 944 . 2 ((𝜑𝜏𝜓) → (𝜑𝜓))
2 3adantl.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylan 278 1 (((𝜑𝜏𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 927
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 929
This theorem is referenced by:  3ad2antl1  1108  nnmord  6316  ltaprg  7275  lediv2a  8453  zdiv  8933  neiint  12012  cnpnei  12085
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