Theorem r19.29aOLD 3332

Description: Obsolete proof of r19.29a 3288 as of 17-Jun-2023. (Contributed by Thierry Arnoux, 22-Nov-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
r19.29aOLD.1	⊢ (((𝜑 ∧ 𝑥 ∈ 𝐴) ∧ 𝜓) → 𝜒)
r19.29aOLD.2	⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓)

Assertion

Ref	Expression
r19.29aOLD	⊢ (𝜑 → 𝜒)

Distinct variable groups:   𝜒,𝑥   𝜑,𝑥

Allowed substitution hints:   𝜓(𝑥)   𝐴(𝑥)

Proof of Theorem r19.29aOLD

Step	Hyp	Ref	Expression
1		nfv 1914	. 2 ⊢ Ⅎ𝑥𝜑
2		r19.29aOLD.1	. 2 ⊢ (((𝜑 ∧ 𝑥 ∈ 𝐴) ∧ 𝜓) → 𝜒)
3		r19.29aOLD.2	. 2 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓)
4	1, 2, 3	r19.29af 3330	1 ⊢ (𝜑 → 𝜒)

Syntax hints:   → wi 4   ∧ wa 398   ∈ wcel 2113  ∃wrex 3138

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-12 2176

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1780  df-nf 1784  df-ral 3142  df-rex 3143

This theorem is referenced by: (None)