Theorem bnj1351 30897

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypothesis

Ref	Expression
bnj1351.1	|- ( ph -> A. x ph )

Assertion

Ref	Expression
bnj1351	|- ( ( ph /\ ps ) -> A. x ( ph /\ ps ) )

Distinct variable group:   ps, x

Allowed substitution hint:   ph( x)

Proof of Theorem bnj1351

Step	Hyp	Ref	Expression
1		bnj1351.1	. 2 |- ( ph -> A. x ph )
2		ax-5 1839	. 2 |- ( ps -> A. x ps )
3	1, 2	hban 2128	1 |- ( ( ph /\ ps ) -> A. x ( ph /\ ps ) )

Syntax hints:   -> wi 4   /\ 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  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710

This theorem is referenced by:  bnj1373  31098  bnj1445  31112