Theorem syl9r 73

Description: A nested syllogism inference with different antecedents. (Contributed by NM, 5-Aug-1993.)

Hypotheses

Ref	Expression
syl9r.1	|- ( ph -> ( ps -> ch ) )
syl9r.2	|- ( th -> ( ch -> ta ) )

Assertion

Ref	Expression
syl9r	|- ( th -> ( ph -> ( ps -> ta ) ) )

Proof of Theorem syl9r

Step	Hyp	Ref	Expression
1		syl9r.1	. . 3 |- ( ph -> ( ps -> ch ) )
2		syl9r.2	. . 3 |- ( th -> ( ch -> ta ) )
3	1, 2	syl9 72	. 2 |- ( ph -> ( th -> ( ps -> ta ) ) )
4	3	com12 30	1 |- ( th -> ( ph -> ( ps -> ta ) ) )

This proof depends on syntax axioms:   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is used by:  sylan9r  414  const  864  pm2.85dc  917  looinvdc  927  pclem6  1423  nfimd  1638  19.23t  1729  fununi  5449  dfimafn  5751  funimass3  5825  dfimafnf  5955  nnsub  9343  bj-con1st  16779