Theorem mpteq2i 4202

Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 16-Dec-2013.)

Hypothesis

Ref	Expression
mpteq2i.1	⊢ 𝐵 = 𝐶

Assertion

Ref	Expression
mpteq2i	⊢ (𝑥 ∈ 𝐴 ↦ 𝐵) = (𝑥 ∈ 𝐴 ↦ 𝐶)

Proof of Theorem mpteq2i

Step	Hyp	Ref	Expression
1		mpteq2i.1	. . 3 ⊢ 𝐵 = 𝐶
2	1	a1i 9	. 2 ⊢ (𝑥 ∈ 𝐴 → 𝐵 = 𝐶)
3	2	mpteq2ia 4201	1 ⊢ (𝑥 ∈ 𝐴 ↦ 𝐵) = (𝑥 ∈ 𝐴 ↦ 𝐶)

Syntax hints:   = wceq 1398   ∈ wcel 2205   ↦ cmpt 4176

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-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-ral 2527  df-opab 4177  df-mpt 4178

This theorem is referenced by:  frecsuc  6651  fodjuomni  7453  fodjumkv  7464  axcaucvg  8231  0tonninf  10826  1tonninf  10827  cbvsum  12070  cbvprod  12269  eirraplem  12488  ballotfilemfc0  13176  ballotfilemfcc  13177  ballotfi  13226  znzrh2  14920  cnmpt12f  15277  fsumcncntop  15558  dvmptfsum  15716  dvef  15718  plyco  15750  plycj  15752  nninfsellemqall  16919  nninfomni  16923  nnnninfex  16926  exmidsbthr  16929