Theorem feq2i 5219

Description: Equality inference for functions. (Contributed by set.mm contributors, 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 5212	. 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 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-11 1746  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-fn 4791  df-f 4792

This theorem is referenced by:  fmpt2x  5731  fmpt2  5732