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Theorem 3adant3r2 1174
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 17-Feb-2008.)
Hypothesis
Ref Expression
3exp.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant3r2 ((𝜑 ∧ (𝜓𝜏𝜒)) → 𝜃)

Proof of Theorem 3adant3r2
StepHypRef Expression
1 3exp.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213expb 1165 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
323adantr2 1124 1 ((𝜑 ∧ (𝜓𝜏𝜒)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 947
This theorem is referenced by:  mettri2  12348  mettri  12359  xmetrtri  12362
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