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Theorem 3adantr3 1076
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
Hypothesis
Ref Expression
3adantr.1 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
Assertion
Ref Expression
3adantr3 ((𝜑 ∧ (𝜓𝜒𝜏)) → 𝜃)

Proof of Theorem 3adantr3
StepHypRef Expression
1 3simpa 912 . 2 ((𝜓𝜒𝜏) → (𝜓𝜒))
2 3adantr.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylan2 274 1 ((𝜑 ∧ (𝜓𝜒𝜏)) → 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:  3ad2antr1  1080  3ad2antr2  1081  3adant3r3  1126  isosolem  5491  caovlem2d  5721
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