Theorem bj-ssbimi 31812

Description: Distribute substitution over implication. Uses only ax-1--5. (Contributed by BJ, 22-Dec-2020.)

Hypothesis

Ref	Expression
bj-ssbimi.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
bj-ssbimi	⊢ ([𝑡/𝑥]b𝜑 → [𝑡/𝑥]b𝜓)

Proof of Theorem bj-ssbimi

Step	Hyp	Ref	Expression
1		bj-ssbim 31810	. 2 ⊢ (∀𝑥(𝜑 → 𝜓) → ([𝑡/𝑥]b𝜑 → [𝑡/𝑥]b𝜓))
2		bj-ssbimi.1	. 2 ⊢ (𝜑 → 𝜓)
3	1, 2	mpg 1715	1 ⊢ ([𝑡/𝑥]b𝜑 → [𝑡/𝑥]b𝜓)

Syntax hints:   → wi 4  [wssb 31808

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827

This theorem depends on definitions:  df-bi 196  df-ssb 31809

This theorem is referenced by: (None)