This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem 19.28

Description: Theorem 19.28 of Margaris p. 90. See 19.28v for a version requiring fewer axioms. (Contributed by NM, 1-Aug-1993) (Proof shortened by Wolf Lammen, 7-May-2025)

Ref Expression
Hypothesis 19.28.1 
|- F/ x ph
Assertion 19.28 
|- ( A. x ( ph /\ ps ) <-> ( ph /\ A. x ps ) )

Proof

Step Hyp Ref Expression
1 19.28.1 
 |-  F/ x ph
2 19.26 
 |-  ( A. x ( ph /\ ps ) <-> ( A. x ph /\ A. x ps ) )
3 1 19.3 
 |-  ( A. x ph <-> ph )
4 2 3 bianbi 
 |-  ( A. x ( ph /\ ps ) <-> ( ph /\ A. x ps ) )