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Mirrors > Home > MPE Home > Th. List > Mathboxes > axfrege52c | Structured version Visualization version GIF version |
Description: Justification for ax-frege52c 40112. (Contributed by RP, 24-Dec-2019.) |
Ref | Expression |
---|---|
axfrege52c | ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsbcq 3771 | . 2 ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 ↔ [𝐵 / 𝑥]𝜑)) | |
2 | 1 | biimpd 230 | 1 ⊢ (𝐴 = 𝐵 → ([𝐴 / 𝑥]𝜑 → [𝐵 / 𝑥]𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 = wceq 1528 [wsbc 3769 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-ext 2790 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 df-cleq 2811 df-clel 2890 df-sbc 3770 |
This theorem is referenced by: (None) |
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