Theorem cbvex2vOLD 2276

Description: Obsolete proof of cbvex2v 2275 as of 18-Jul-2021. (Contributed by NM, 26-Jul-1995.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
cbval2v.1	⊢ ((𝑥 = 𝑧 ∧ 𝑦 = 𝑤) → (𝜑 ↔ 𝜓))

Assertion

Ref	Expression
cbvex2vOLD	⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑧∃𝑤𝜓)

Distinct variable groups:   𝑧,𝑤,𝜑   𝑥,𝑦,𝜓   𝑥,𝑤   𝑦,𝑧

Allowed substitution hints:   𝜑(𝑥,𝑦)   𝜓(𝑧,𝑤)

Proof of Theorem cbvex2vOLD

Step	Hyp	Ref	Expression
1		nfv 1830	. 2 ⊢ Ⅎ𝑧𝜑
2		nfv 1830	. 2 ⊢ Ⅎ𝑤𝜑
3		nfv 1830	. 2 ⊢ Ⅎ𝑥𝜓
4		nfv 1830	. 2 ⊢ Ⅎ𝑦𝜓
5		cbval2v.1	. 2 ⊢ ((𝑥 = 𝑧 ∧ 𝑦 = 𝑤) → (𝜑 ↔ 𝜓))
6	1, 2, 3, 4, 5	cbvex2 2268	1 ⊢ (∃𝑥∃𝑦𝜑 ↔ ∃𝑧∃𝑤𝜓)

Syntax hints:   → wi 4   ↔ wb 195   ∧ wa 383  ∃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  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701

This theorem is referenced by: (None)