Mathbox for Thierry Arnoux < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  19.9d2rf Unicode version

Theorem 19.9d2rf 23956
 Description: A deduction version of one direction of 19.9 1797 with two variables (Contributed by Thierry Arnoux, 20-Mar-2017.)
Hypotheses
Ref Expression
19.9d2rf.0
19.9d2rf.1
19.9d2rf.2
19.9d2rf.3
Assertion
Ref Expression
19.9d2rf

Proof of Theorem 19.9d2rf
StepHypRef Expression
1 19.9d2rf.3 . . . 4
2 rexex 2757 . . . 4
3 rexex 2757 . . . . 5
43eximi 1585 . . . 4
51, 2, 43syl 19 . . 3
6 19.9d2rf.0 . . . . 5
7 19.9d2rf.1 . . . . 5
86, 7nfexd 1873 . . . 4
9819.9d 1796 . . 3
105, 9mpd 15 . 2
11 19.9d2rf.2 . . 3
121119.9d 1796 . 2
1310, 12mpd 15 1
 Colors of variables: wff set class Syntax hints:   wi 4  wex 1550  wnf 1553  wrex 2698 This theorem is referenced by:  19.9d2r  23957  xrofsup  24114 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-6 1744  ax-7 1749  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554  df-rex 2703
 Copyright terms: Public domain W3C validator