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Theorem 3ad2antl1 1101
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 461 . 2 (((𝜑𝜏) ∧ 𝜒) → 𝜃)
323adantl2 1096 1 (((𝜑𝜓𝜏) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 920
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 922
This theorem is referenced by:  acexmid  5563  ordiso2  6541  addlocpr  6824  distrlem1prl  6870  distrlem1pru  6871  ltsopr  6884  addcanprlemu  6903  fzo1fzo0n0  9305  expival  9611  muldvds2  10413  dvds2add  10421  dvds2sub  10422  dvdstr  10424
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