Theorem prlem1OLD 1092

Description: Obsolete proof of prlem1 1091.

Hypotheses

Ref	Expression
prlem1.1	|- (ph -> (et <-> ch))
prlem1.2	|- (ps -> -. th)

Assertion

Ref	Expression
prlem1OLD	|- (ph -> (ps -> (((ps /\ ch) \/ (th /\ ta)) -> et)))

Proof of Theorem prlem1OLD

Step	Hyp	Ref	Expression
1		prlem1.1	. . . . . 6 |- (ph -> (et <-> ch))
2	1	biimprd 232	. . . . 5 |- (ph -> (ch -> et))
3	2	adantld 450	. . . 4 |- (ph -> ((ps /\ ch) -> et))
4	3	adantr 447	. . 3 |- ((ph /\ ps) -> ((ps /\ ch) -> et))
5		prlem1.2	. . . . . 6 |- (ps -> -. th)
6	5	pm2.21d 123	. . . . 5 |- (ps -> (th -> et))
7	6	adantrd 452	. . . 4 |- (ps -> ((th /\ ta) -> et))
8	7	adantl 448	. . 3 |- ((ph /\ ps) -> ((th /\ ta) -> et))
9	4, 8	jaod 454	. 2 |- ((ph /\ ps) -> (((ps /\ ch) \/ (th /\ ta)) -> et))
10	9	ex 398	1 |- (ph -> (ps -> (((ps /\ ch) \/ (th /\ ta)) -> et)))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 219   \/ wo 336   /\ wa 337

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 220  df-or 338  df-an 339

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