Theorem ifeq12 1782

Description: Equality theorem for conditional operators.

Assertion

Ref	Expression
ifeq12	|- ((A = B /\ C = D) -> if(ph, A, C) = if(ph, B, D))

Proof of Theorem ifeq12

Step	Hyp	Ref	Expression
1		ifeq1 1778	. 2 |- (A = B -> if(ph, A, C) = if(ph, B, C))
2		ifeq2 1779	. 2 |- (C = D -> if(ph, B, C) = if(ph, B, D))
3	1, 2	sylan9eq 1144	1 |- ((A = B /\ C = D) -> if(ph, A, C) = if(ph, B, D))

Syntax hints:   -> wi 2   /\ wa 196   = wceq 1091  ifcif 1776

This theorem is referenced by:  unxpdomlem 3649  ruclem4 4888  ruclem15 4899

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925  ax-ext 1074

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-clab 1093  df-cleq 1097  df-clel 1099  df-if 1777

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