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Theorem iffalsei 3882
Description: Inference associated with iffalse 3881. (Contributed by BJ, 7-Oct-2018.)
Hypothesis
Ref Expression
iffalsei.1  |-  -.  ph
Assertion
Ref Expression
iffalsei  |-  if (
ph ,  A ,  B )  =  B

Proof of Theorem iffalsei
StepHypRef Expression
1 iffalsei.1 . 2  |-  -.  ph
2 iffalse 3881 . 2  |-  ( -. 
ph  ->  if ( ph ,  A ,  B )  =  B )
31, 2ax-mp 5 1  |-  if (
ph ,  A ,  B )  =  B
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    = wceq 1452   ifcif 3872
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451
This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-if 3873
This theorem is referenced by:  sum0  13864  prod0  14074  prmo4  15177  prmo6  15179  itg0  22816  vieta1lem2  23343  dfrdg2  30513  dfrdg4  30789  fwddifnp1  31003  bj-pr21val  31677  bj-pr22val  31683  refsum2cnlem1  37421  iblempty  37939  fouriersw  38207  vtxval0  39292  iedgval0  39293
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