Theorem ifeq12 3958

Description: Equality theorem for conditional operators. (Contributed by NM, 1-Sep-2004.)

Assertion

Ref	Expression
ifeq12

Proof of Theorem ifeq12

Step	Hyp	Ref	Expression
1		ifeq1 3945	. 2
2		ifeq2 3946	. 2
3	1, 2	sylan9eq 2518	1

Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  ifcif 3941

This theorem is referenced by:  xaddmnf1  11456  xpslem  14970  ditg0  22257  mumullem2  23454

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