Theorem nfmod 2219

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

Hypotheses

Ref	Expression
nfeud.1	|- F/yph
nfeud.2	|- (ph -> F/xps)

Assertion

Ref	Expression
nfmod	|- (ph -> F/xE*yps)

Proof of Theorem nfmod

Step	Hyp	Ref	Expression
1		nfeud.1	. 2 |- F/yph
2		nfeud.2	. . 3 |- (ph -> F/xps)
3	2	adantr 451	. 2 |- ((ph /\ -. A.x x = y) -> F/xps)
4	1, 3	nfmod2 2217	1 |- (ph -> F/xE*yps)

This proof depends on syntax axioms:  -. wn 3   -> wi 4  A.wal 1540   F/wnf 1544   = wceq 1642  E*wmo 2205

This proof depends on 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 proof 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 used by:  nfmo  2221