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Theorem 3ad2antr2 1132
Description: Deduction adding a conjuncts to antecedent. (Contributed by NM, 27-Dec-2007.)
Hypothesis
Ref Expression
3ad2antl.1 ((𝜑𝜒) → 𝜃)
Assertion
Ref Expression
3ad2antr2 ((𝜑 ∧ (𝜓𝜒𝜏)) → 𝜃)

Proof of Theorem 3ad2antr2
StepHypRef Expression
1 3ad2antl.1 . . 3 ((𝜑𝜒) → 𝜃)
21adantrl 469 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
323adantr3 1127 1 ((𝜑 ∧ (𝜓𝜒𝜏)) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  w3a 947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by:  prarloclem  7277  ioc0  10008
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