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

Theorem adantrlr 703
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)
Hypothesis
Ref Expression
adantr2.1 ((φ (ψ χ)) → θ)
Assertion
Ref Expression
adantrlr ((φ ((ψ τ) χ)) → θ)

Proof of Theorem adantrlr
StepHypRef Expression
1 simpl 443 . 2 ((ψ τ) → ψ)
2 adantr2.1 . 2 ((φ (ψ χ)) → θ)
31, 2sylanr1 633 1 ((φ ((ψ τ) χ)) → θ)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
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
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator