Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  spcgf Structured version   Unicode version

Theorem spcgf 3032
 Description: Rule of specialization, using implicit substitution. Compare Theorem 7.3 of [Quine] p. 44. (Contributed by NM, 2-Feb-1997.) (Revised by Andrew Salmon, 12-Aug-2011.)
Hypotheses
Ref Expression
spcgf.1
spcgf.2
spcgf.3
Assertion
Ref Expression
spcgf

Proof of Theorem spcgf
StepHypRef Expression
1 spcgf.2 . . 3
2 spcgf.1 . . 3
31, 2spcgft 3029 . 2
4 spcgf.3 . 2
53, 4mpg 1558 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550  wnf 1554   wceq 1653   wcel 1726  wnfc 2560 This theorem is referenced by:  spcegf  3033  spcgv  3037  rspc  3047  elabgt  3080  eusvnf  4719  sumeq2w  12487  prodeq2w  25239 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-v 2959
 Copyright terms: Public domain W3C validator