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Theorem ax10lem2 1877
 Description: Lemma for ax10 1884. Change free variable. (Contributed by NM, 25-Jul-2015.)
Assertion
Ref Expression
ax10lem2
Distinct variable groups:   ,   ,

Proof of Theorem ax10lem2
StepHypRef Expression
1 hbe1 1705 . . . 4
2 equequ2 1649 . . . . . . . 8
32biimprd 214 . . . . . . 7
43con3rr3 128 . . . . . 6
5 19.8a 1718 . . . . . 6
64, 5syl6 29 . . . . 5
7 ax-17 1603 . . . . . 6
8 equequ1 1648 . . . . . . . 8
98notbid 285 . . . . . . 7
109biimprd 214 . . . . . 6
117, 10spimeh 1722 . . . . 5
126, 11pm2.61d1 151 . . . 4
131, 12exlimih 1729 . . 3
14 exnal 1561 . . 3
15 exnal 1561 . . 3
1613, 14, 153imtr3i 256 . 2
1716con4i 122 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1527  wex 1528 This theorem is referenced by:  ax10lem3  1878 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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