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Theorem ax10lem2 2023
 Description: Lemma for ax10 2025. Change bound variable. (Contributed by NM, 8-Jul-2016.) (Proof shortened by Wolf Lammen, 17-Feb-2018.)
Assertion
Ref Expression
ax10lem2
Distinct variable groups:   ,   ,

Proof of Theorem ax10lem2
StepHypRef Expression
1 ax10lem1 2022 . . 3
2 equequ2 1698 . . . . 5
32biimprd 215 . . . 4
43al2imi 1570 . . 3
51, 4syl5com 28 . 2
6 dveeq1 2021 . . . . 5
76spsd 1771 . . . 4
87com12 29 . . 3
98con1d 118 . 2
105, 9pm2.61d 152 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1549 This theorem is referenced by:  ax10  2025  aevlem1  2046 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  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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