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Theorem 3adantl2 1139
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 980 . 2 ((𝜑𝜏𝜓) → (𝜑𝜓))
2 3adantl.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylan 281 1 (((𝜑𝜏𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 965
This theorem is referenced by:  3ad2antl1  1144  nnmord  6417  ltaprg  7447  lediv2a  8673  zdiv  9159  neiint  12344  cnpnei  12418
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