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Theorem hbaes 1608
Description: Rule that applies hbae 1606 to antecedent. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
hbalequs.1 (∀𝑧𝑥 𝑥 = 𝑦𝜑)
Assertion
Ref Expression
hbaes (∀𝑥 𝑥 = 𝑦𝜑)

Proof of Theorem hbaes
StepHypRef Expression
1 hbae 1606 . 2 (∀𝑥 𝑥 = 𝑦 → ∀𝑧𝑥 𝑥 = 𝑦)
2 hbalequs.1 . 2 (∀𝑧𝑥 𝑥 = 𝑦𝜑)
31, 2syl 14 1 (∀𝑥 𝑥 = 𝑦𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1241
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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