Theorem nfmo 2221

Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 9-Mar-1995.)

Hypothesis

Ref	Expression
nfeu.1	|- F/xph

Assertion

Ref	Expression
nfmo	|- F/xE*yph

Proof of Theorem nfmo

Step	Hyp	Ref	Expression
1		nftru 1554	. . 3 |- F/y T.
2		nfeu.1	. . . 4 |- F/xph
3	2	a1i 10	. . 3 |- ( T. -> F/xph)
4	1, 3	nfmod 2219	. 2 |- ( T. -> F/xE*yph)
5	4	trud 1323	1 |- F/xE*yph

Syntax hints:   T. wtru 1316   F/wnf 1544  E*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:  moexex  2273  2moex  2275  2euex  2276  mosubopt  4613  dffun6f  5124