NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  3adant3r1 GIF version

Theorem 3adant3r1 1160
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 16-Feb-2008.)
Hypothesis
Ref Expression
3exp.1 ((φ ψ χ) → θ)
Assertion
Ref Expression
3adant3r1 ((φ (τ ψ χ)) → θ)

Proof of Theorem 3adant3r1
StepHypRef Expression
1 3exp.1 . . 3 ((φ ψ χ) → θ)
213expb 1152 . 2 ((φ (ψ χ)) → θ)
323adantr1 1114 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: (None)
  Copyright terms: Public domain W3C validator