Theorem 19.27OLD 2222

Description: Obsolete proof of 19.27 2082 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 1786	. 2 ⊢ (∀𝑥(𝜑 ∧ 𝜓) ↔ (∀𝑥𝜑 ∧ ∀𝑥𝜓))
2		19.27OLD.1	. . . 4 ⊢ Ⅎ𝑥𝜓
3	2	19.3OLD 2190	. . 3 ⊢ (∀𝑥𝜓 ↔ 𝜓)
4	3	anbi2i 726	. 2 ⊢ ((∀𝑥𝜑 ∧ ∀𝑥𝜓) ↔ (∀𝑥𝜑 ∧ 𝜓))
5	1, 4	bitri 263	1 ⊢ (∀𝑥(𝜑 ∧ 𝜓) ↔ (∀𝑥𝜑 ∧ 𝜓))

Syntax hints:   ↔ wb 195   ∧ wa 383  ∀wal 1473  ℲwnfOLD 1700

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-12 2034

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-nfOLD 1712

This theorem is referenced by: (None)