ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  3ad2antl1 Structured version   GIF version

Theorem 3ad2antl1 1052
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 449 . 2 (((φ τ) χ) → θ)
323adantl2 1047 1 (((φ ψ τ) χ) → θ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97   w3a 871
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110  df-3an 873
This theorem is referenced by:  acexmid  5431  addlocpr  6385  distrlem1prl  6415  distrlem1pru  6416  ltsopr  6427  addcanprleml  6445  addcanprlemu  6446
  Copyright terms: Public domain W3C validator