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Theorem 3adant3r3 1150
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 18-Feb-2008.)
Hypothesis
Ref Expression
3exp.1 ((𝜑𝜓𝜒) → 𝜃)
Assertion
Ref Expression
3adant3r3 ((𝜑 ∧ (𝜓𝜒𝜏)) → 𝜃)

Proof of Theorem 3adant3r3
StepHypRef Expression
1 3exp.1 . . 3 ((𝜑𝜓𝜒) → 𝜃)
213expb 1140 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
323adantr3 1100 1 ((𝜑 ∧ (𝜓𝜒𝜏)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115  df-3an 922
This theorem is referenced by: (None)
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