Theorem hbaes 1708

Description: Rule that applies hbae 1706 to antecedent. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
hbalequs.1	⊢ (∀𝑧∀𝑥 𝑥 = 𝑦 → 𝜑)

Assertion

Ref	Expression
hbaes	⊢ (∀𝑥 𝑥 = 𝑦 → 𝜑)

Proof of Theorem hbaes

Step	Hyp	Ref	Expression
1		hbae 1706	. 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑧∀𝑥 𝑥 = 𝑦)
2		hbalequs.1	. 2 ⊢ (∀𝑧∀𝑥 𝑥 = 𝑦 → 𝜑)
3	1, 2	syl 14	1 ⊢ (∀𝑥 𝑥 = 𝑦 → 𝜑)

Syntax hints:   → wi 4  ∀wal 1341

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)