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Theorem 3adantr2 1115
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)
Hypothesis
Ref Expression
3adantr.1 ((φ (ψ χ)) → θ)
Assertion
Ref Expression
3adantr2 ((φ (ψ τ χ)) → θ)

Proof of Theorem 3adantr2
StepHypRef Expression
1 3simpb 953 . 2 ((ψ τ χ) → (ψ χ))
2 3adantr.1 . 2 ((φ (ψ χ)) → θ)
31, 2sylan2 460 1 ((φ (ψ τ χ)) → θ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358   w3a 934
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  3adant3r2  1161
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