Theorem bnj937 35069

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

Hypothesis

Ref	Expression
bnj937.1	⊢ (𝜑 → ∃𝑥𝜓)

Assertion

Ref	Expression
bnj937	⊢ (𝜑 → 𝜓)

Distinct variable group:   𝜓,𝑥

Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem bnj937

Step	Hyp	Ref	Expression
1		bnj937.1	. 2 ⊢ (𝜑 → ∃𝑥𝜓)
2		19.9v 2006	. 2 ⊢ (∃𝑥𝜓 ↔ 𝜓)
3	1, 2	sylib 220	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1801

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989

This theorem depends on definitions:  df-bi 209  df-ex 1802

This theorem is referenced by:  bnj1265  35109  bnj1379  35127  bnj852  35218  bnj1148  35293  bnj1154  35296  bnj1189  35306  bnj1245  35311  bnj1286  35316  bnj1311  35321  bnj1371  35326  bnj1374  35328  bnj1498  35358  bnj1514  35360