Theorem aevALTOLD 2321

Description: Older alternate proof of aev 1983. Obsolete as of 30-Mar-2021. (Contributed by NM, 8-Nov-2006.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
aevALTOLD	⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧 𝑤 = 𝑣)

Distinct variable group:   𝑥,𝑦

Proof of Theorem aevALTOLD

Dummy variable 𝑢 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		hbae 2315	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)
2		aevlem 1981	. . 3 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑢 𝑢 = 𝑣)
3		ax7 1943	. . . 4 ⊢ (𝑢 = 𝑤 → (𝑢 = 𝑣 → 𝑤 = 𝑣))
4	3	spimv 2257	. . 3 ⊢ (∀𝑢 𝑢 = 𝑣 → 𝑤 = 𝑣)
5	2, 4	syl 17	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → 𝑤 = 𝑣)
6	1, 5	alrimih 1751	1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧 𝑤 = 𝑣)

Syntax hints:   → wi 4  ∀wal 1481

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-10 2019  ax-11 2034  ax-12 2047  ax-13 2246

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710

This theorem is referenced by: (None)