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

Theorem dvelimALT 2209
 Description: Version of dvelim 2069 that doesn't use ax-10 2216. (See dvelimh 2067 for a version that doesn't use ax-11 1761.) (Contributed by NM, 17-May-2008.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
dvelimALT.1
dvelimALT.2
Assertion
Ref Expression
dvelimALT
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,,)   (,)

Proof of Theorem dvelimALT
StepHypRef Expression
1 ax-17 1626 . . 3
2 ax16ALT 2131 . . . . 5
32a1d 23 . . . 4
4 hbn1 1745 . . . . . . 7
5 hbn1 1745 . . . . . . 7
64, 5hban 1850 . . . . . 6
7 ax12o 2010 . . . . . . 7
87imp 419 . . . . . 6
9 dvelimALT.1 . . . . . . 7
109a1i 11 . . . . . 6
116, 8, 10hbimd 1834 . . . . 5
1211ex 424 . . . 4
133, 12pm2.61i 158 . . 3
141, 13hbald 1755 . 2
15 ax-17 1626 . . 3
16 dvelimALT.2 . . 3
1715, 16equsalh 2001 . 2
1817albii 1575 . 2
1914, 17, 183imtr3g 261 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359  wal 1549 This theorem is referenced by:  dveeq2-o16  2261 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  df-sb 1659
 Copyright terms: Public domain W3C validator