Theorem bnj1024 13808

Description: First-order logic and set theory.

Hypotheses

Ref	Expression
bnj1024.1	|- E.xph
bnj1024.2	|- ps

Assertion

Ref	Expression
bnj1024	|- E.x(ph /\ ps)

Proof of Theorem bnj1024

Step	Hyp	Ref	Expression
1		bnj1024.2	. . . 4 |- ps
2	1	a1i 8	. . 3 |- (ph -> ps)
3	2	ax-gen 1622	. 2 |- A.x(ph -> ps)
4		bnj1024.1	. 2 |- E.xph
5		exintr 1786	. 2 |- (A.x(ph -> ps) -> (E.xph -> E.x(ph /\ ps)))
6	3, 4, 5	mp2 98	1 |- E.x(ph /\ ps)

Syntax hints:   -> wi 3   /\ wa 433  A.wal 1613  E.wex 1644

This theorem is referenced by:  bnj1025 13809  bnj1023 13810  bnj1102 13848

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1622  ax-4 1637  ax-5o 1639

This theorem depends on definitions:  df-bi 232  df-an 435  df-ex 1645

Copyright terms: Public domain