Theorem bj-genan 32593

Description: Generalization rule on a conjunction. Forward inference associated with 19.26 1798. (Contributed by BJ, 7-Jul-2021.)

Hypothesis

Ref	Expression
bj-genr.1	|- ( ph /\ ps )

Assertion

Ref	Expression
bj-genan	|- ( A. x ph /\ A. x ps )

Proof of Theorem bj-genan

Step	Hyp	Ref	Expression
1		bj-genr.1	. . . 4 |- ( ph /\ ps )
2	1	simpli 474	. . 3 |- ph
3	2	ax-gen 1722	. 2 |- A. x ph
4	1	simpri 478	. . 3 |- ps
5	4	ax-gen 1722	. 2 |- A. x ps
6	3, 5	pm3.2i 471	1 |- ( A. x ph /\ A. x ps )

Syntax hints:   /\ wa 384   A.wal 1481

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

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

This theorem is referenced by: (None)