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Theorem bj-sbimeh 9355
Description: A strengthening of sbieh 1673 (same proof). (Contributed by BJ, 16-Dec-2019.)
Hypotheses
Ref Expression
bj-sbimeh.1 (ψxψ)
bj-sbimeh.2 (x = y → (φψ))
Assertion
Ref Expression
bj-sbimeh ([y / x]φψ)

Proof of Theorem bj-sbimeh
StepHypRef Expression
1 tru 1247 . . . 4
21hbth 1352 . . 3 ( ⊤ → x ⊤ )
3 bj-sbimeh.1 . . . 4 (ψxψ)
43a1i 9 . . 3 ( ⊤ → (ψxψ))
5 bj-sbimeh.2 . . . 4 (x = y → (φψ))
65a1i 9 . . 3 ( ⊤ → (x = y → (φψ)))
72, 4, 6bj-sbimedh 9354 . 2 ( ⊤ → ([y / x]φψ))
87trud 1252 1 ([y / x]φψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1241  wtru 1244  [wsb 1645
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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-sb 1646
This theorem is referenced by:  bj-sbime  9356
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