Theorem aev2ALT 1987

Description: Alternate proof of aev2 1986, bypassing hbaevg 1984. (Contributed by BJ, 23-Mar-2021.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
aev2ALT	⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑡 𝑢 = 𝑣)

Distinct variable group:   𝑥,𝑦

Proof of Theorem aev2ALT

Dummy variables 𝑤 𝑠 are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		aev 1983	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑤 𝑤 = 𝑠)
2		aev 1983	. . 3 ⊢ (∀𝑤 𝑤 = 𝑠 → ∀𝑡 𝑢 = 𝑣)
3	2	alrimiv 1855	. 2 ⊢ (∀𝑤 𝑤 = 𝑠 → ∀𝑧∀𝑡 𝑢 = 𝑣)
4	1, 3	syl 17	1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑡 𝑢 = 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

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by: (None)