Theorem ifbieq12i 3967

Description: Equivalence deduction for conditional operators. (Contributed by NM, 18-Mar-2013.)

Hypotheses

Ref	Expression
ifbieq12i.1
ifbieq12i.2
ifbieq12i.3

Assertion

Ref	Expression
ifbieq12i

Proof of Theorem ifbieq12i

Step	Hyp	Ref	Expression
1		ifbieq12i.2	. . 3
2		ifeq1 3945	. . 3
3	1, 2	ax-mp 5	. 2
4		ifbieq12i.1	. . 3
5		ifbieq12i.3	. . 3
6	4, 5	ifbieq2i 3965	. 2
7	3, 6	eqtri 2486	1

Syntax hints:  <->wb 184  =wceq 1395  ifcif 3941

This theorem is referenced by:  cbvditg  22258  sgnneg  28479  binomcxplemdvsum  31260

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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-un 3480  df-if 3942