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Theorem 3ad2antr2 1069
Description: Deduction adding a conjuncts to antecedent. (Contributed by NM, 27-Dec-2007.)
Hypothesis
Ref Expression
3ad2antl.1 ((φ χ) → θ)
Assertion
Ref Expression
3ad2antr2 ((φ (ψ χ τ)) → θ)

Proof of Theorem 3ad2antr2
StepHypRef Expression
1 3ad2antl.1 . . 3 ((φ χ) → θ)
21adantrl 447 . 2 ((φ (ψ χ)) → θ)
323adantr3 1064 1 ((φ (ψ χ τ)) → θ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   w3a 884
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 886
This theorem is referenced by:  prarloclem  6476
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