Theorem dedth3h 3995

Description: Weak deduction theorem eliminating three hypotheses. See comments in dedth2h 3994. (Contributed by NM, 15-May-1999.)

Hypotheses

Ref	Expression
dedth3h.1
dedth3h.2
dedth3h.3
dedth3h.4

Assertion

Ref	Expression
dedth3h

Proof of Theorem dedth3h

Step	Hyp	Ref	Expression
1		dedth3h.1	. . . 4
2	1	imbi2d 316	. . 3
3		dedth3h.2	. . . 4
4		dedth3h.3	. . . 4
5		dedth3h.4	. . . 4
6	3, 4, 5	dedth2h 3994	. . 3
7	2, 6	dedth 3993	. 2
8	7	3impib 1194	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  =wceq 1395  ifcif 3941

This theorem is referenced by:  dedth3v  3998  faclbnd4lem2  12372  dvdsle  14031  gcdaddm  14167  ipdiri  25745  hvaddcan  25987  hvsubadd  25994  norm3dif  26067  omlsii  26321  chjass  26451  ledi  26458  spansncv  26571  pjcjt2  26610  pjopyth  26638  hoaddass  26701  hocsubdir  26704  hoddi  26909

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-if 3942