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Theorem adantrrr 464
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)
Hypothesis
Ref Expression
adantr2.1 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
Assertion
Ref Expression
adantrrr ((𝜑 ∧ (𝜓 ∧ (𝜒𝜏))) → 𝜃)

Proof of Theorem adantrrr
StepHypRef Expression
1 simpl 106 . 2 ((𝜒𝜏) → 𝜒)
2 adantr2.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylanr2 391 1 ((𝜑 ∧ (𝜓 ∧ (𝜒𝜏))) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101
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 is referenced by:  2ndconst  5871  genpdisj  6679  ltexprlemdisj  6762  addsrmo  6886  mulsrmo  6887  lemul12b  7902
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