Theorem bnj937 34764

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 1981	. 2 ⊢ (∃𝑥𝜓 ↔ 𝜓)
3	1, 2	sylib 218	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965

This theorem depends on definitions:  df-bi 207  df-ex 1777

This theorem is referenced by:  bnj1265  34805  bnj1379  34823  bnj852  34914  bnj1148  34989  bnj1154  34992  bnj1189  35002  bnj1245  35007  bnj1286  35012  bnj1311  35017  bnj1371  35022  bnj1374  35024  bnj1498  35054  bnj1514  35056