Theorem fv2 5325

Description: Alternate definition of function value. Definition 10.11 of [Quine] p. 68. (The proof was shortened by Andrew Salmon, 17-Sep-2011.) (Contributed by set.mm contributors, 30-Apr-2004.) (Revised by set.mm contributors, 18-Sep-2011.)

Assertion

Ref	Expression
fv2	⊢ (F ‘A) = ∪{x ∣ ∀y(AFy ↔ y = x)}

Distinct variable groups:   x,y,A   x,F,y

Proof of Theorem fv2

Step	Hyp	Ref	Expression
1		df-fv 4796	. 2 ⊢ (F ‘A) = (℩yAFy)
2		dfiota2 4341	. 2 ⊢ (℩yAFy) = ∪{x ∣ ∀y(AFy ↔ y = x)}
3	1, 2	eqtri 2373	1 ⊢ (F ‘A) = ∪{x ∣ ∀y(AFy ↔ y = x)}

Syntax hints:   ↔ wb 176  ∀wal 1540   = wceq 1642  {cab 2339  ∪cuni 3892  ℩cio 4338   class class class wbr 4640   ‘cfv 4782

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-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2479  df-rex 2621  df-sn 3742  df-uni 3893  df-iota 4340  df-fv 4796

This theorem is referenced by:  elfv  5327