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Theorem 3adant2r 1177
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 8-Jan-2006.)
Hypothesis
Ref Expression
3adant1l.1 ((φ ψ χ) → θ)
Assertion
Ref Expression
3adant2r ((φ (ψ τ) χ) → θ)

Proof of Theorem 3adant2r
StepHypRef Expression
1 3adant1l.1 . . . 4 ((φ ψ χ) → θ)
213com12 1155 . . 3 ((ψ φ χ) → θ)
323adant1r 1175 . 2 (((ψ τ) φ χ) → θ)
433com12 1155 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: (None)
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