Theorem feq2i 5428

Description: Equality inference for functions. (Contributed by NM, 5-Sep-2011.)

Hypothesis

Ref	Expression
feq2i.1	⊢ 𝐴 = 𝐵

Assertion

Ref	Expression
feq2i	⊢ (𝐹:𝐴⟶𝐶 ↔ 𝐹:𝐵⟶𝐶)

Proof of Theorem feq2i

Step	Hyp	Ref	Expression
1		feq2i.1	. 2 ⊢ 𝐴 = 𝐵
2		feq2 5418	. 2 ⊢ (𝐴 = 𝐵 → (𝐹:𝐴⟶𝐶 ↔ 𝐹:𝐵⟶𝐶))
3	1, 2	ax-mp 5	1 ⊢ (𝐹:𝐴⟶𝐶 ↔ 𝐹:𝐵⟶𝐶)

Syntax hints:   ↔ wb 105   = wceq 1373  ⟶wf 5275

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 1471  ax-gen 1473  ax-4 1534  ax-17 1550  ax-ext 2188

This theorem depends on definitions:  df-bi 117  df-cleq 2199  df-fn 5282  df-f 5283

This theorem is referenced by:  fmpox  6298  fmpo  6299  tposf  6370  issmo  6386  tfrcllemsucfn  6451  1fv  10276  fxnn0nninf  10601  snopiswrd  11021  iswrddm0  11035  0met  14926  dvef  15269  uhgr0e  15748