Theorem funeqi 5128

Description: Equality inference for the function predicate. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypothesis

Ref	Expression
funeqi.1	⊢ A = B

Assertion

Ref	Expression
funeqi	⊢ (Fun A ↔ Fun B)

Proof of Theorem funeqi

Step	Hyp	Ref	Expression
1		funeqi.1	. 2 ⊢ A = B
2		funeq 5127	. 2 ⊢ (A = B → (Fun A ↔ Fun B))
3	1, 2	ax-mp 5	1 ⊢ (Fun A ↔ Fun B)

Syntax hints:   ↔ wb 176   = wceq 1642  Fun wfun 4775

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 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-opab 4623  df-br 4640  df-co 4726  df-cnv 4785  df-fun 4789

This theorem is referenced by:  funco  5142  funprg  5149  funprgOLD  5150  funcnvuni  5161  funcnvres2  5167  f1co  5264  fun11iun  5305  f10  5316  funoprabg  5583  ovidig  5593  funmpt  5687  enpw1  6062  sbthlem3  6205