Theorem exanOLD 1789

Description: Obsolete proof of exan 1788 as of 8-Oct-2021. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 13-Jan-2018.) Reduce axiom dependencies. (Revised by BJ, 7-Jul-2021.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
exan.1	|- ( E. x ph /\ ps )

Assertion

Ref	Expression
exanOLD	|- E. x ( ph /\ ps )

Proof of Theorem exanOLD

Step	Hyp	Ref	Expression
1		exan.1	. . 3 |- ( E. x ph /\ ps )
2	1	simpli 474	. 2 |- E. x ph
3		pm3.21 464	. . . 4 |- ( ps -> ( ph -> ( ph /\ ps ) ) )
4	3	aleximi 1759	. . 3 |- ( A. x ps -> ( E. x ph -> E. x ( ph /\ ps ) ) )
5	1	simpri 478	. . 3 |- ps
6	4, 5	mpg 1724	. 2 |- ( E. x ph -> E. x ( ph /\ ps ) )
7	2, 6	ax-mp 5	1 |- E. x ( ph /\ ps )

Syntax hints:   -> wi 4   /\ wa 384   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by: (None)