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Theorem ax16ALT 1736
 Description: Version of ax16 1691 that doesn't require ax-10 1393 or ax-12 1399 for its proof. (Contributed by NM, 17-May-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax16ALT (x x = y → (φxφ))
Distinct variable group:   x,y
Allowed substitution hints:   φ(x,y)

Proof of Theorem ax16ALT
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 sbequ12 1651 . 2 (x = z → (φ ↔ [z / x]φ))
2 ax-17 1416 . . 3 (φzφ)
32hbsb3 1686 . 2 ([z / x]φx[z / x]φ)
41, 3ax16i 1735 1 (x x = y → (φxφ))
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1240  [wsb 1642 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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643 This theorem is referenced by:  dvelimALT  1883  dvelimfv  1884
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