Theorem nfeud 2218

Description: Deduction version of nfeu 2220. (Contributed by NM, 15-Feb-2013.) (Revised by Mario Carneiro, 7-Oct-2016.)

Hypotheses

Ref	Expression
nfeud.1	⊢ Ⅎyφ
nfeud.2	⊢ (φ → Ⅎxψ)

Assertion

Ref	Expression
nfeud	⊢ (φ → Ⅎx∃!yψ)

Proof of Theorem nfeud

Step	Hyp	Ref	Expression
1		nfeud.1	. 2 ⊢ Ⅎyφ
2		nfeud.2	. . 3 ⊢ (φ → Ⅎxψ)
3	2	adantr 451	. 2 ⊢ ((φ ∧ ¬ ∀x x = y) → Ⅎxψ)
4	1, 3	nfeud2 2216	1 ⊢ (φ → Ⅎx∃!yψ)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540  Ⅎwnf 1544   = wceq 1642  ∃!weu 2204

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

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-eu 2208

This theorem is referenced by:  nfeu  2220