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

Theorem spv 1737
Description: Specialization, using implicit substitition. (Contributed by NM, 30-Aug-1993.)
Hypothesis
Ref Expression
spv.1 (x = y → (φψ))
Assertion
Ref Expression
spv (xφψ)
Distinct variable group:   ψ,x
Allowed substitution hints:   φ(x,y)   ψ(y)

Proof of Theorem spv
StepHypRef Expression
1 spv.1 . . 3 (x = y → (φψ))
21biimpd 132 . 2 (x = y → (φψ))
32spimv 1689 1 (xφψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1240
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  chvarv  1809  ru  2757  nalset  3878  tfisi  4253  bj-nalset  9326
  Copyright terms: Public domain W3C validator