Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  cbv3hv Structured version   Unicode version

Theorem cbv3hv 1878
 Description: Lemma for ax10 2025. Similar to cbv3h 1972. Requires distinct variables but avoids ax-12 1950. (Contributed by NM, 25-Jul-2015.) (Proof shortened by Wolf Lammen, 29-Dec-2017.)
Hypotheses
Ref Expression
cbv3hv.1
cbv3hv.2
cbv3hv.3
Assertion
Ref Expression
cbv3hv
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbv3hv
StepHypRef Expression
1 cbv3hv.1 . . 3
21alimi 1568 . 2
3 a9ev 1668 . . . . . . 7
4 cbv3hv.3 . . . . . . 7
53, 4eximii 1587 . . . . . 6
6519.35i 1611 . . . . 5
7 cbv3hv.2 . . . . . 6
8719.9h 1794 . . . . 5
96, 8sylib 189 . . . 4
109alimi 1568 . . 3
1110a7s 1750 . 2
122, 11syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1549  wex 1550 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
 Copyright terms: Public domain W3C validator