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Theorem 3adant2r 1222
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
Hypothesis
Ref Expression
3adant1l.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant2r ((𝜑 ∧ (𝜓𝜏) ∧ 𝜒) → 𝜃)

Proof of Theorem 3adant2r
StepHypRef Expression
1 3adant1l.1 . . . 4 ((𝜑𝜓𝜒) → 𝜃)
213com12 1196 . . 3 ((𝜓𝜑𝜒) → 𝜃)
323adant1r 1220 . 2 (((𝜓𝜏) ∧ 𝜑𝜒) → 𝜃)
433com12 1196 1 ((𝜑 ∧ (𝜓𝜏) ∧ 𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 967
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 969
This theorem is referenced by:  caovimo  6027  mulassnqg  7317  prarloc  7436  ltexprlemfl  7542  ltexprlemfu  7544  addasssrg  7689  axaddass  7805
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