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Theorem 2sbbii 2075
Description: Infer double substitution into both sides of a logical equivalence. (Contributed by AV, 30-Jul-2023.)
Hypothesis
Ref Expression
sbbii.1 (𝜑𝜓)
Assertion
Ref Expression
2sbbii ([𝑡 / 𝑥][𝑢 / 𝑦]𝜑 ↔ [𝑡 / 𝑥][𝑢 / 𝑦]𝜓)

Proof of Theorem 2sbbii
StepHypRef Expression
1 sbbii.1 . . 3 (𝜑𝜓)
21sbbii 2074 . 2 ([𝑢 / 𝑦]𝜑 ↔ [𝑢 / 𝑦]𝜓)
32sbbii 2074 1 ([𝑡 / 𝑥][𝑢 / 𝑦]𝜑 ↔ [𝑡 / 𝑥][𝑢 / 𝑦]𝜓)
Colors of variables: wff setvar class
Syntax hints:  wb 207  [wsb 2062
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803
This theorem depends on definitions:  df-bi 208  df-sb 2063
This theorem is referenced by:  sbco4lem  2277  ichcircshi  43440  ichbi12i  43446  icheq  43448  ichal  43455
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