Metamath Proof Explorer


Theorem nfralwOLD

Description: Obsolete version of nfralw as of 13-Dec-2024. (Contributed by NM, 1-Sep-1999) (Revised by Gino Giotto, 10-Jan-2024) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses nfralw.1
|- F/_ x A
nfralw.2
|- F/ x ph
Assertion nfralwOLD
|- F/ x A. y e. A ph

Proof

Step Hyp Ref Expression
1 nfralw.1
 |-  F/_ x A
2 nfralw.2
 |-  F/ x ph
3 nftru
 |-  F/ y T.
4 1 a1i
 |-  ( T. -> F/_ x A )
5 2 a1i
 |-  ( T. -> F/ x ph )
6 3 4 5 nfraldw
 |-  ( T. -> F/ x A. y e. A ph )
7 6 mptru
 |-  F/ x A. y e. A ph