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Theorem fneq2i 5179
 Description: Equality inference for function predicate with domain. (Contributed by set.mm contributors, 4-Sep-2011.)
Hypothesis
Ref Expression
fneq2i.1 A = B
Assertion
Ref Expression
fneq2i (F Fn AF Fn B)

Proof of Theorem fneq2i
StepHypRef Expression
1 fneq2i.1 . 2 A = B
2 fneq2 5174 . 2 (A = B → (F Fn AF Fn B))
31, 2ax-mp 5 1 (F Fn AF Fn B)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 176   = wceq 1642   Fn wfn 4776 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-fn 4790 This theorem is referenced by:  fnunsn  5190  ovg  5601  fncup  5813  addcfn  5825  fncross  5846  fnmap  6007  fnpm  6008  xpassen  6057  fnce  6176
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