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Theorem ifeq1d 3676
 Description: Equality deduction for conditional operator. (Contributed by NM, 16-Feb-2005.)
Hypothesis
Ref Expression
ifeq1d.1 (φA = B)
Assertion
Ref Expression
ifeq1d (φ → if(ψ, A, C) = if(ψ, B, C))

Proof of Theorem ifeq1d
StepHypRef Expression
1 ifeq1d.1 . 2 (φA = B)
2 ifeq1 3666 . 2 (A = B → if(ψ, A, C) = if(ψ, B, C))
31, 2syl 15 1 (φ → if(ψ, A, C) = if(ψ, B, C))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1642   ifcif 3662 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rab 2623  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-if 3663 This theorem is referenced by:  ifeq12d  3678  ifeq1da  3687
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