Theorem nfmod 2219

Description: Bound-variable hypothesis builder for "at most one." (Contributed by Mario Carneiro, 14-Nov-2016.)

Hypotheses

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

Assertion

Ref	Expression
nfmod	⊢ (φ → Ⅎx∃*yψ)

Proof of Theorem nfmod

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	nfmod2 2217	1 ⊢ (φ → Ⅎx∃*yψ)

Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540  Ⅎwnf 1544   = wceq 1642  ∃*wmo 2205

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  df-mo 2209

This theorem is referenced by:  nfmo  2221