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Theorem 3adantl2 1112
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)
Hypothesis
Ref Expression
3adantl.1 (((φ ψ) χ) → θ)
Assertion
Ref Expression
3adantl2 (((φ τ ψ) χ) → θ)

Proof of Theorem 3adantl2
StepHypRef Expression
1 3simpb 953 . 2 ((φ τ ψ) → (φ ψ))
2 3adantl.1 . 2 (((φ ψ) χ) → θ)
31, 2sylan 457 1 (((φ τ ψ) 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:  3ad2antl1  1117
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