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Theorem fneq1i 5212
 Description: Equality inference for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011.)
Hypothesis
Ref Expression
fneq1i.1 𝐹 = 𝐺
Assertion
Ref Expression
fneq1i (𝐹 Fn 𝐴𝐺 Fn 𝐴)

Proof of Theorem fneq1i
StepHypRef Expression
1 fneq1i.1 . 2 𝐹 = 𝐺
2 fneq1 5206 . 2 (𝐹 = 𝐺 → (𝐹 Fn 𝐴𝐺 Fn 𝐴))
31, 2ax-mp 5 1 (𝐹 Fn 𝐴𝐺 Fn 𝐴)
 Colors of variables: wff set class Syntax hints:   ↔ wb 104   = wceq 1331   Fn wfn 5113 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-sn 3528  df-pr 3529  df-op 3531  df-br 3925  df-opab 3985  df-rel 4541  df-cnv 4542  df-co 4543  df-dm 4544  df-fun 5120  df-fn 5121 This theorem is referenced by:  fnunsn  5225  fnopabg  5241  f1oun  5380  f1oi  5398  f1osn  5400  ovid  5880  tfri1d  6225  frec2uzrand  10171  frec2uzf1od  10172  frecfzennn  10192  nninfsellemeqinf  13201
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