ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  a2i Structured version   GIF version

Theorem a2i 11
Description: Inference derived from axiom ax-2 6. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
a2i.1 (φ → (ψχ))
Assertion
Ref Expression
a2i ((φψ) → (φχ))

Proof of Theorem a2i
StepHypRef Expression
1 a2i.1 . 2 (φ → (ψχ))
2 ax-2 6 . 2 ((φ → (ψχ)) → ((φψ) → (φχ)))
31, 2ax-mp 7 1 ((φψ) → (φχ))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-2 6  ax-mp 7
This theorem is referenced by:  imim2i  12  mpd  13  sylcom  25  pm2.43  47  ancl  301  ancr  304  anc2r  311  pm2.65  584  pm2.18dc  749  con4biddc  753  hbim1  1459  sbcof2  1688  ralimia  2376  ceqsalg  2576  rspct  2643  elabgt  2678  fvmptt  5205  bj-exlimmp  9244  bj-rspgt  9260  bj-indint  9390
  Copyright terms: Public domain W3C validator