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Theorem 3adantl2 1061
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 902 . 2 ((𝜑𝜏𝜓) → (𝜑𝜓))
2 3adantl.1 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
31, 2sylan 267 1 (((𝜑𝜏𝜓) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97  w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by:  3ad2antl1  1066  nnmord  6090  ltaprg  6715  lediv2a  7859  zdiv  8326
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