Theorem feq2i 5507

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 5497	. 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 1398  ⟶wf 5353

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-gen 1498  ax-4 1559  ax-17 1575  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-cleq 2227  df-fn 5360  df-f 5361

This theorem is referenced by:  fmpox  6409  fmpo  6410  tposf  6516  issmo  6532  tfrcllemsucfn  6597  1fv  10495  fxnn0nninf  10825  snopiswrd  11259  iswrddm0  11273  0met  15361  dvef  15704  uhgr0e  16189  vtxdumgrfival  16405  gfsum0  16976