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

Theorem spcv 2945
Description: Rule of specialization, using implicit substitution. (Contributed by NM, 22-Jun-1994.)
Hypotheses
Ref Expression
spcv.1 A V
spcv.2 (x = A → (φψ))
Assertion
Ref Expression
spcv (xφψ)
Distinct variable groups:   x,A   ψ,x
Allowed substitution hint:   φ(x)

Proof of Theorem spcv
StepHypRef Expression
1 spcv.1 . 2 A V
2 spcv.2 . . 3 (x = A → (φψ))
32spcgv 2939 . 2 (A V → (xφψ))
41, 3ax-mp 5 1 (xφψ)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wal 1540   = wceq 1642   wcel 1710  Vcvv 2859
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861
This theorem is referenced by:  morex  3020  nnsucelr  4428  ssrel  4844
  Copyright terms: Public domain W3C validator