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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-ssbimi | Structured version Visualization version GIF version |
Description: Distribute substitution over implication. Uses only ax-1--5. (Contributed by BJ, 22-Dec-2020.) |
Ref | Expression |
---|---|
bj-ssbimi.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
bj-ssbimi | ⊢ ([𝑡/𝑥]b𝜑 → [𝑡/𝑥]b𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-ssbim 32621 | . 2 ⊢ (∀𝑥(𝜑 → 𝜓) → ([𝑡/𝑥]b𝜑 → [𝑡/𝑥]b𝜓)) | |
2 | bj-ssbimi.1 | . 2 ⊢ (𝜑 → 𝜓) | |
3 | 1, 2 | mpg 1724 | 1 ⊢ ([𝑡/𝑥]b𝜑 → [𝑡/𝑥]b𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 [wssb 32619 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 |
This theorem depends on definitions: df-bi 197 df-ssb 32620 |
This theorem is referenced by: (None) |
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