Theorem feq23i 5220

Description: Equality inference for functions. (Contributed by Paul Chapman, 22-Jun-2011.)

Hypotheses

Ref	Expression
feq23i.1	⊢ A = C
feq23i.2	⊢ B = D

Assertion

Ref	Expression
feq23i	⊢ (F:A–→B ↔ F:C–→D)

Proof of Theorem feq23i

Step	Hyp	Ref	Expression
1		feq23i.1	. 2 ⊢ A = C
2		feq23i.2	. 2 ⊢ B = D
3		feq23 5214	. 2 ⊢ ((A = C ∧ B = D) → (F:A–→B ↔ F:C–→D))
4	1, 2, 3	mp2an 653	1 ⊢ (F:A–→B ↔ F:C–→D)

Syntax hints:   ↔ wb 176   = wceq 1642  –→wf 4778

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-v 2862  df-nin 3212  df-compl 3213  df-in 3214  df-ss 3260  df-fn 4791  df-f 4792

This theorem is referenced by: (None)