NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  3adant3r GIF version

Theorem 3adant3r 1179
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
3adant3r ((φ ψ (χ τ)) → θ)

Proof of Theorem 3adant3r
StepHypRef Expression
1 3adant1l.1 . . . 4 ((φ ψ χ) → θ)
213com13 1156 . . 3 ((χ ψ φ) → θ)
323adant1r 1175 . 2 (((χ τ) ψ φ) → θ)
433com13 1156 1 ((φ ψ (χ τ)) → 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)
  Copyright terms: Public domain W3C validator