Theorem nfimOLD 1814

Description: If x is not free in ph and ps, it is not free in (ph -> ps). (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
nfim.1	|- F/xph
nfim.2	|- F/xps

Assertion

Ref	Expression
nfimOLD	|- F/x(ph -> ps)

Proof of Theorem nfimOLD

Step	Hyp	Ref	Expression
1		nfim.1	. . . 4 |- F/xph
2	1	a1i 10	. . 3 |- ( T. -> F/xph)
3		nfim.2	. . . 4 |- F/xps
4	3	a1i 10	. . 3 |- ( T. -> F/xps)
5	2, 4	nfimd 1808	. 2 |- ( T. -> F/x(ph -> ps))
6	5	trud 1323	1 |- F/x(ph -> ps)

Syntax hints:   -> wi 4   T. wtru 1316   F/wnf 1544

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-11 1746

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

This theorem is referenced by: (None)