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Theorem fconst6 5441
Description: A constant function as a mapping. (Contributed by Jeff Madsen, 30-Nov-2009.) (Revised by Mario Carneiro, 22-Apr-2015.)
Hypothesis
Ref Expression
fconst6.1 𝐵𝐶
Assertion
Ref Expression
fconst6 (𝐴 × {𝐵}):𝐴𝐶

Proof of Theorem fconst6
StepHypRef Expression
1 fconst6.1 . 2 𝐵𝐶
2 fconst6g 5440 . 2 (𝐵𝐶 → (𝐴 × {𝐵}):𝐴𝐶)
31, 2ax-mp 5 1 (𝐴 × {𝐵}):𝐴𝐶
Colors of variables: wff set class
Syntax hints:  wcel 2160  {csn 3614   × cxp 4649  wf 5238
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2163  ax-ext 2171  ax-sep 4143  ax-pow 4199  ax-pr 4234
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-nf 1472  df-sb 1774  df-eu 2041  df-mo 2042  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rex 2474  df-v 2758  df-un 3153  df-in 3155  df-ss 3162  df-pw 3599  df-sn 3620  df-pr 3621  df-op 3623  df-br 4026  df-opab 4087  df-mpt 4088  df-id 4318  df-xp 4657  df-rel 4658  df-cnv 4659  df-co 4660  df-dm 4661  df-rn 4662  df-fun 5244  df-fn 5245  df-f 5246
This theorem is referenced by:  0ct  7152  ctm  7154  infnninfOLD  7170  exmidomni  7187  ofnegsub  8967  0nninf  15418  exmidsbthrlem  15436
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