Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  r19.37 Unicode version

Theorem r19.37 2849
 Description: Restricted version of one direction of Theorem 19.37 of [Margaris] p. 90. (The other direction doesn't hold when is empty.) (Contributed by FL, 13-May-2012.) (Revised by Mario Carneiro, 11-Dec-2016.)
Hypothesis
Ref Expression
r19.37.1
Assertion
Ref Expression
r19.37

Proof of Theorem r19.37
StepHypRef Expression
1 r19.35 2847 . 2
2 r19.37.1 . . . 4
3 ax-1 5 . . . 4
42, 3ralrimi 2779 . . 3
54imim1i 56 . 2
61, 5sylbi 188 1
 Colors of variables: wff set class Syntax hints:   wi 4  wnf 1553   wcel 1725  wral 2697  wrex 2698 This theorem is referenced by:  r19.37av  2850 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-ral 2702  df-rex 2703
 Copyright terms: Public domain W3C validator