Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.21 Structured version   Visualization version   Unicode version

Theorem 19.21 1987
 Description: Theorem 19.21 of [Margaris] p. 90. The hypothesis can be thought of as " is not free in ." See 19.21v 1786 for a version requiring fewer axioms. See also 19.21h 1989. (Contributed by NM, 14-May-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.21.1
Assertion
Ref Expression
19.21

Proof of Theorem 19.21
StepHypRef Expression
1 19.21.1 . 2
2 19.21t 1986 . 2
31, 2ax-mp 5 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188  wal 1442  wnf 1667 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-12 1933 This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-nf 1668 This theorem is referenced by:  19.21-2  1988  19.21h  1989  stdpc5  1990  nf3  2042  19.32  2047  19.21vOLD  2071  19.12vv  2076  cbv1  2110  axc14  2201  r2alf  2764  r2alfOLD  2765  19.12b  30448  bj-biexal2  31300  bj-bialal  31302  bj-cbv1v  31330  wl-dral1d  31864  mpt2bi123f  32406
 Copyright terms: Public domain W3C validator