Theorem nfmpt1 5673

Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by FL, 17-Feb-2008.)

Assertion

Ref	Expression
nfmpt1	⊢ Ⅎx(x ∈ A ↦ B)

Proof of Theorem nfmpt1

Dummy variable z is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-mpt 5653	. 2 ⊢ (x ∈ A ↦ B) = {⟨x, z⟩ ∣ (x ∈ A ∧ z = B)}
2		nfopab1 4629	. 2 ⊢ Ⅎx{⟨x, z⟩ ∣ (x ∈ A ∧ z = B)}
3	1, 2	nfcxfr 2487	1 ⊢ Ⅎx(x ∈ A ↦ B)

Syntax hints:   ∧ wa 358   = wceq 1642   ∈ wcel 1710  Ⅎwnfc 2477  {copab 4623   ↦ cmpt 5652

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-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-opab 4624  df-mpt 5653

This theorem is referenced by:  fvmptss  5706  fvmptf  5723