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Theorem 3ad2antl1 1077
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)
Hypothesis
Ref Expression
3ad2antl.1 ((𝜑𝜒) → 𝜃)
Assertion
Ref Expression
3ad2antl1 (((𝜑𝜓𝜏) ∧ 𝜒) → 𝜃)

Proof of Theorem 3ad2antl1
StepHypRef Expression
1 3ad2antl.1 . . 3 ((𝜑𝜒) → 𝜃)
21adantlr 454 . 2 (((𝜑𝜏) ∧ 𝜒) → 𝜃)
323adantl2 1072 1 (((𝜑𝜓𝜏) ∧ 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:  acexmid  5538  ordiso2  6414  addlocpr  6691  distrlem1prl  6737  distrlem1pru  6738  ltsopr  6751  addcanprlemu  6770  fzo1fzo0n0  9140  expival  9416  muldvds2  10125  dvds2add  10133  dvds2sub  10134  dvdstr  10136
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