Theorem exanOLDOLD 2169

Description: Obsolete proof of exan 1788 as of 7-Jul-2021. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.) (Proof shortened by Wolf Lammen, 13-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
exanOLDOLD.1	⊢ (∃𝑥𝜑 ∧ 𝜓)

Assertion

Ref	Expression
exanOLDOLD	⊢ ∃𝑥(𝜑 ∧ 𝜓)

Proof of Theorem exanOLDOLD

Step	Hyp	Ref	Expression
1		exanOLDOLD.1	. 2 ⊢ (∃𝑥𝜑 ∧ 𝜓)
2	1	simpri 478	. . . 4 ⊢ 𝜓
3	2	nfth 1727	. . 3 ⊢ Ⅎ𝑥𝜓
4	3	19.41 2103	. 2 ⊢ (∃𝑥(𝜑 ∧ 𝜓) ↔ (∃𝑥𝜑 ∧ 𝜓))
5	1, 4	mpbir 221	1 ⊢ ∃𝑥(𝜑 ∧ 𝜓)

Syntax hints:   ∧ wa 384  ∃wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)