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Theorem bj-ssbimi 32992
Description: Distribute substitution over implication. Uses only ax-1--5. (Contributed by BJ, 22-Dec-2020.)
Hypothesis
Ref Expression
bj-ssbimi.1 (𝜑𝜓)
Assertion
Ref Expression
bj-ssbimi ([𝑡/𝑥]b𝜑 → [𝑡/𝑥]b𝜓)

Proof of Theorem bj-ssbimi
StepHypRef Expression
1 bj-ssbim 32990 . 2 (∀𝑥(𝜑𝜓) → ([𝑡/𝑥]b𝜑 → [𝑡/𝑥]b𝜓))
2 bj-ssbimi.1 . 2 (𝜑𝜓)
31, 2mpg 1892 1 ([𝑡/𝑥]b𝜑 → [𝑡/𝑥]b𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  [wssb 32988
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005
This theorem depends on definitions:  df-bi 198  df-ssb 32989
This theorem is referenced by: (None)
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