Theorem 19.27OLD 2234

Description: Obsolete proof of 19.27 2095 as of 6-Oct-2021. (Contributed by NM, 21-Jun-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
19.27OLD.1	⊢ Ⅎ𝑥𝜓

Assertion

Ref	Expression
19.27OLD	⊢ (∀𝑥(𝜑 ∧ 𝜓) ↔ (∀𝑥𝜑 ∧ 𝜓))

Proof of Theorem 19.27OLD

Step	Hyp	Ref	Expression
1		19.26 1798	. 2 ⊢ (∀𝑥(𝜑 ∧ 𝜓) ↔ (∀𝑥𝜑 ∧ ∀𝑥𝜓))
2		19.27OLD.1	. . . 4 ⊢ Ⅎ𝑥𝜓
3	2	19.3OLD 2202	. . 3 ⊢ (∀𝑥𝜓 ↔ 𝜓)
4	3	anbi2i 730	. 2 ⊢ ((∀𝑥𝜑 ∧ ∀𝑥𝜓) ↔ (∀𝑥𝜑 ∧ 𝜓))
5	1, 4	bitri 264	1 ⊢ (∀𝑥(𝜑 ∧ 𝜓) ↔ (∀𝑥𝜑 ∧ 𝜓))

Syntax hints:   ↔ wb 196   ∧ wa 384  ∀wal 1481  ℲwnfOLD 1709

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-nfOLD 1721

This theorem is referenced by: (None)