NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  3ad2antr2 GIF version

Theorem 3ad2antr2 1121
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 27-Dec-2007.)
Hypothesis
Ref Expression
3ad2antl.1 ((φ χ) → θ)
Assertion
Ref Expression
3ad2antr2 ((φ (ψ χ τ)) → θ)

Proof of Theorem 3ad2antr2
StepHypRef Expression
1 3ad2antl.1 . . 3 ((φ χ) → θ)
21adantrl 696 . 2 ((φ (ψ χ)) → θ)
323adantr3 1116 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