Theorem bnj937 30096

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 1883	. 2 ⊢ (∃𝑥𝜓 ↔ 𝜓)
3	1, 2	sylib 207	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1695

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875

This theorem depends on definitions:  df-bi 196  df-ex 1696

This theorem is referenced by:  bnj1265  30137  bnj1379  30155  bnj852  30245  bnj1148  30318  bnj1154  30321  bnj1189  30331  bnj1245  30336  bnj1286  30341  bnj1311  30346  bnj1371  30351  bnj1374  30353  bnj1498  30383  bnj1514  30385