Theorem bnj937 34969

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 1992	. 2 ⊢ (∃𝑥𝜓 ↔ 𝜓)
3	1, 2	sylib 220	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1787

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1975

This theorem depends on definitions:  df-bi 209  df-ex 1788

This theorem is referenced by:  bnj1265  35009  bnj1379  35027  bnj852  35118  bnj1148  35193  bnj1154  35196  bnj1189  35206  bnj1245  35211  bnj1286  35216  bnj1311  35221  bnj1371  35226  bnj1374  35228  bnj1498  35258  bnj1514  35260