Theorem feq2i 5261

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 5251	. 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 104   = wceq 1331  ⟶wf 5114

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 1423  ax-gen 1425  ax-4 1487  ax-17 1506  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-cleq 2130  df-fn 5121  df-f 5122

This theorem is referenced by:  fmpox  6091  fmpo  6092  tposf  6162  issmo  6178  tfrcllemsucfn  6243  1fv  9909  fxnn0nninf  10204  0met  12542  dvef  12845