NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  3ad2antl1 GIF version

Theorem 3ad2antl1 1117
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)
Hypothesis
Ref Expression
3ad2antl.1 ((φ χ) → θ)
Assertion
Ref Expression
3ad2antl1 (((φ ψ τ) χ) → θ)

Proof of Theorem 3ad2antl1
StepHypRef Expression
1 3ad2antl.1 . . 3 ((φ χ) → θ)
21adantlr 695 . 2 (((φ τ) χ) → θ)
323adantl2 1112 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-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
This theorem is referenced by:  sfintfin  4532  ce2le  6233
  Copyright terms: Public domain W3C validator