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Theorem feq3d 5229
 Description: Equality deduction for functions. (Contributed by AV, 1-Jan-2020.)
Hypothesis
Ref Expression
feq2d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
feq3d (𝜑 → (𝐹:𝑋𝐴𝐹:𝑋𝐵))

Proof of Theorem feq3d
StepHypRef Expression
1 feq2d.1 . 2 (𝜑𝐴 = 𝐵)
2 feq3 5225 . 2 (𝐴 = 𝐵 → (𝐹:𝑋𝐴𝐹:𝑋𝐵))
31, 2syl 14 1 (𝜑 → (𝐹:𝑋𝐴𝐹:𝑋𝐵))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 104   = wceq 1314  ⟶wf 5087 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-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-in 3045  df-ss 3052  df-f 5095 This theorem is referenced by:  uptx  12349  txcn  12350
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