Theorem bnj1299 13044

Description: First-order logic and set theory.

Hypothesis

Ref	Expression
bnj1299.1	|- (ph -> E.x e. A (ps /\ ch))

Assertion

Ref	Expression
bnj1299	|- (ph -> E.x e. A ps)

Proof of Theorem bnj1299

Step	Hyp	Ref	Expression
1		bnj1299.1	. 2 |- (ph -> E.x e. A (ps /\ ch))
2		bnj1239 13007	. 2 |- (E.x e. A (ps /\ ch) -> E.x e. A ps)
3	1, 2	syl 12	1 |- (ph -> E.x e. A ps)

Syntax hints:   -> wi 3   /\ wa 240  E.wrex 2106

This theorem is referenced by:  bnj1497 13560  bnj1498 13562  bnj1516 13566

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-4 1319  ax-5o 1321

This theorem depends on definitions:  df-bi 164  df-an 242  df-ex 1327  df-ral 2109  df-rex 2110

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