Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax11inda2ALT Structured version   Unicode version

Theorem ax11inda2ALT 2275
 Description: A proof of ax11inda2 2276 that is slightly more direct. (Contributed by NM, 4-May-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ax11inda2.1
Assertion
Ref Expression
ax11inda2ALT
Distinct variable group:   ,
Allowed substitution hints:   (,,)

Proof of Theorem ax11inda2ALT
StepHypRef Expression
1 ax-1 5 . . . . . . . 8
21a5i-o 2227 . . . . . . 7
32a1i 11 . . . . . 6
4 biidd 229 . . . . . . 7
54dral1-o 2231 . . . . . 6
65imbi2d 308 . . . . . . 7
76dral2-o 2258 . . . . . 6
83, 5, 73imtr4d 260 . . . . 5
98aecoms-o 2229 . . . 4
109a1d 23 . . 3
1110a1d 23 . 2
12 simplr 732 . . . . 5
13 dveeq1-o 2264 . . . . . . . 8
1413naecoms-o 2255 . . . . . . 7
1514imp 419 . . . . . 6
1615adantlr 696 . . . . 5
17 hbnae-o 2256 . . . . . . 7
18 hba1-o 2226 . . . . . . 7
1917, 18hban 1850 . . . . . 6
20 ax-4 2212 . . . . . . 7
21 ax11inda2.1 . . . . . . . 8
2221imp 419 . . . . . . 7
2320, 22sylan2 461 . . . . . 6
2419, 23alimdh 1572 . . . . 5
2512, 16, 24syl2anc 643 . . . 4
26 ax-7 1749 . . . . . 6
27 hbnae-o 2256 . . . . . . 7
28 hbnae-o 2256 . . . . . . . . 9
2928, 14nfdh 1783 . . . . . . . 8
30 19.21t 1813 . . . . . . . 8
3129, 30syl 16 . . . . . . 7
3227, 31albidh 1600 . . . . . 6
3326, 32syl5ib 211 . . . . 5
3433ad2antrr 707 . . . 4
3525, 34syld 42 . . 3
3635exp31 588 . 2
3711, 36pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359  wal 1549  wnf 1553 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  ax-4 2212  ax-5o 2213  ax-6o 2214  ax-10o 2216  ax-12o 2219 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
 Copyright terms: Public domain W3C validator