Theorem exgenOLD 1979

Description: Obsolete version of exgen 1978 as of 20-Oct-2023. (Contributed by Wolf Lammen, 12-Nov-2017.) (Proof shortened by Wolf Lammen, 9-Dec-2017.) (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
exgen.1	⊢ 𝜑

Assertion

Ref	Expression
exgenOLD	⊢ ∃𝑥𝜑

Proof of Theorem exgenOLD

Dummy variable 𝑦 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ax6ev 1972	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		exgen.1	. . 3 ⊢ 𝜑
3	2	a1i 11	. 2 ⊢ (𝑥 = 𝑦 → 𝜑)
4	1, 3	eximii 1837	1 ⊢ ∃𝑥𝜑

Syntax hints:  ∃wex 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-6 1970

This theorem depends on definitions:  df-bi 209  df-ex 1781

This theorem is referenced by: (None)