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Theorem fneq1i 4919
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 4913 . 2 (𝐹 = 𝐺 → (𝐹 Fn A𝐺 Fn A))
31, 2ax-mp 7 1 (𝐹 Fn A𝐺 Fn A)
Colors of variables: wff set class
Syntax hints:  wb 98   = wceq 1228   Fn wfn 4824
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-3an 875  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-un 2899  df-in 2901  df-ss 2908  df-sn 3356  df-pr 3357  df-op 3359  df-br 3739  df-opab 3793  df-rel 4279  df-cnv 4280  df-co 4281  df-dm 4282  df-fun 4831  df-fn 4832
This theorem is referenced by:  fnunsn  4932  fnopabg  4948  f1oun  5071  f1oi  5089  f1osn  5091  ovid  5540  tfri1d  5871  tfri1  5873
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