Theorem bnj937 35130

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 2012	. 2 ⊢ (∃𝑥𝜓 ↔ 𝜓)
3	1, 2	sylib 221	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1807

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995

This theorem depends on definitions:  df-bi 210  df-ex 1808

This theorem is referenced by:  bnj1265  35170  bnj1379  35188  bnj852  35279  bnj1148  35354  bnj1154  35357  bnj1189  35367  bnj1245  35372  bnj1286  35377  bnj1311  35382  bnj1371  35387  bnj1374  35389  bnj1498  35419  bnj1514  35421