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Theorem 3adantr2 1064
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
Hypothesis
Ref Expression
3adantr.1 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
Assertion
Ref Expression
3adantr2 ((𝜑 ∧ (𝜓𝜏𝜒)) → 𝜃)

Proof of Theorem 3adantr2
StepHypRef Expression
1 3simpb 902 . 2 ((𝜓𝜏𝜒) → (𝜓𝜒))
2 3adantr.1 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
31, 2sylan2 270 1 ((𝜑 ∧ (𝜓𝜏𝜒)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 97  w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 887
This theorem is referenced by:  3adant3r2  1114  po3nr  4047  isosolem  5463  caovlem2d  5693
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