ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  al2imi Structured version   GIF version

Theorem al2imi 1323
Description: Inference quantifying antecedent, nested antecedent, and consequent. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
al2imi.1 (φ → (ψχ))
Assertion
Ref Expression
al2imi (xφ → (xψxχ))

Proof of Theorem al2imi
StepHypRef Expression
1 al2imi.1 . . 3 (φ → (ψχ))
21alimi 1320 . 2 (xφx(ψχ))
3 alim 1322 . 2 (x(ψχ) → (xψxχ))
42, 3syl 14 1 (xφ → (xψxχ))
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1224
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1312  ax-gen 1314
This theorem is referenced by:  alanimi  1324  alimdh  1332  albi  1333  19.30dc  1496  19.33b2  1498  hbnt  1521  ax10o  1581  spimth  1601  sbi1v  1749  ralim  2354  ceqsalt  2553  intss  3606
  Copyright terms: Public domain W3C validator