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Theorem 19.9d2r 23199
 Description: A deduction version of one direction of 19.9 1795 with two variables (Contributed by Thierry Arnoux, 30-Jan-2017.)
Hypotheses
Ref Expression
19.9d2r.1
19.9d2r.2
19.9d2r.3
Assertion
Ref Expression
19.9d2r
Distinct variable group:   ,
Allowed substitution hints:   ()   (,)   (,)   (,)

Proof of Theorem 19.9d2r
StepHypRef Expression
1 19.9d2r.3 . . . 4
2 rexex 2615 . . . 4
3 rexex 2615 . . . . 5
43eximi 1566 . . . 4
51, 2, 43syl 18 . . 3
6 nfv 1609 . . . . 5
7 19.9d2r.1 . . . . 5
86, 7nfexd 1788 . . . 4
9819.9d 1796 . . 3
105, 9mpd 14 . 2
11 19.9d2r.2 . . 3
121119.9d 1796 . 2
1310, 12mpd 14 1
 Colors of variables: wff set class Syntax hints:   wi 4  wex 1531  wnf 1534  wrex 2557 This theorem is referenced by:  xrofsup  23270 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535  df-rex 2562
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