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Theorem spimeh 1722
 Description: Existential introduction, using implicit substitution. Compare Lemma 14 of [Tarski] p. 70. (Contributed by NM, 7-Aug-1994.)
Hypotheses
Ref Expression
spimeh.1
spimeh.2
Assertion
Ref Expression
spimeh
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem spimeh
StepHypRef Expression
1 ax9v 1636 . . . 4
2 id 19 . . . . . . 7
32hbth 1539 . . . . . . . 8
4 hba1 1719 . . . . . . . . 9
54a1i 10 . . . . . . . 8
6 spimeh.1 . . . . . . . . . 10
76hbn 1720 . . . . . . . . 9
87a1i 10 . . . . . . . 8
93, 5, 8hbimd 1721 . . . . . . 7
102, 9ax-mp 8 . . . . . 6
1110hbn 1720 . . . . 5
12 spimeh.2 . . . . . . 7
13 sp 1716 . . . . . . 7
1412, 13nsyli 133 . . . . . 6
1514con3i 127 . . . . 5
1611, 15alrimih 1552 . . . 4
171, 16mt3 171 . . 3
1817con2i 112 . 2
19 df-ex 1529 . 2
2018, 19sylibr 203 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1527  wex 1528 This theorem is referenced by:  ax12olem1  1868  ax10lem2  1877 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715 This theorem depends on definitions:  df-bi 177  df-ex 1529
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